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Recent questions tagged straight-lines
Questions
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle.
cbse
class11
ch10
bookproblem
straight-lines
misc
sec-b
medium
q17
asked
Jul 11, 2014
by
thanvigandhi_1
1
answer
Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following : The equation of the line through the intersection of the lines 2x – 3y = 0 and4x – 5y = 2 and
cbse
class11
ch10
straight-lines
exemplar
sec-a
q59
asked
Jul 9, 2014
by
thanvigandhi_1
1
answer
Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following : The value of the $ \lambda$, if the lines $(2x + 3y + 4) +\lambda (6x – y + 12) = 0 $ are
cbse
class11
ch10
straight-lines
exemplar
sec-a
medium
q58
asked
Jul 9, 2014
by
thanvigandhi_1
1
answer
Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following :
cbse
class11
ch10
straight-lines
exemplar
sec-a
q57
asked
Jul 9, 2014
by
thanvigandhi_1
1
answer
State whether the following is true or false and justify : Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).
cbse
class11
ch10
straight-lines
exemplar
sec-a
medium
q56
asked
Jul 9, 2014
by
thanvigandhi_1
1
answer
State whether the following statement is true or false and justify : The lines $ ax + 2y + 1 = 0, bx + 3y + 1 = 0 $ and $cx + 4y + 1 = 0$ are concurrent if a, b, c are in G.P
cbse
class11
ch10
straight-lines
exemplar
sec-a
easy
q55
asked
Jul 9, 2014
by
thanvigandhi_1
1
answer
State whether the following statement is true or false and justify : The equation of the line joining the point (3, 5) to the point of intersection of the lines $4x + y – 1 = 0 $ and $7x – 3y – 35 = 0$ is equidistant from the points (0, 0) and (8, 34)
cbse
class11
ch10
straight-lines
exemplar
sec-a
q53
asked
Jul 9, 2014
by
thanvigandhi_1
1
answer
State whether the following statement is true or false and justify : The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is $x + y = 2$. Then the other two sides are $y - 3 = (2 \pm \sqrt3 ) (x - 2)$.
cbse
math
class11
ch10
straight-lines
exemplar
sec-a
easy
q52
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
State whether the following statement is true or false and justify : The straight line $5x + 4y = 0$ passes through the point of intersection of the straight lines $x + 2y – 10 = 0$ and $ 2x + y + 5 = 0$
cbse
math
class11
ch10
straight-lines
exemplar
sec-a
easy
q51
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
State whether the following statement is true or false and justify : Equation of the line passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \sec \theta + y \: cosec \theta = a $ is $ x \cos \theta - y \sin \theta = a \sin 2 \theta $
cbse
math
class11
ch10
straight-lines
exemplar
sec-a
easy
q50
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
State whether the following statement is true or false and justify : The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear
cbse
math
class11
ch10
straight-lines
exemplar
sec-a
easy
q49
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
Fill in the blank for the following : A point moves so that square of its distance from the point (3, –2) is numerically equal to its distance from the line $ 5x – 12y = 3$ . The equation of its locus is ____.
cbse
class11
ch10
straight-lines
exemplar
sec-a
medium
q46
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
Fil in the blank for the following : The points (3, 4) and (2, – 6) are situated on the ____ of the line $3x – 4y – 8 = 0$ .
cbse
class11
ch10
straight-lines
exemplar
sec-a
medium
q45
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
Fill in the blank for the the following : Equations of the lines through the point $(3, 2)$ and making an angle of $ 45^{\circ}$ with the line $x-2y=3 $ are _______.
cbse
class11
ch10
straight-lines
exemplar
sec-a
medium
q44
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
Fill in the bank for the following : the line which cuts off equal intercept from the axes and pass through the point (1, -2) is _________.
cbse
class11
ch10
straight-lines
exemplar
sec-a
medium
q43
asked
Jul 8, 2014
by
thanvigandhi_1
1
answer
Fill in the blank for the following : If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ____.
cbse
math
class11
ch10
straight-lines
exemplar
sec-a
easy
q42
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is \[\] [Hint: Let ABC be the equilateral triangle with vertex A (h, k) and let D ($ \alpha , \beta $ ) be the point on BC. Then $ \large\frac{2\alpha + h}{3}$$=0 = \large\frac{2\beta + k}{3}$. Also $ \alpha + \beta -2 = 0$ and $ \bigg( \large\frac{k-0}{h-0} \bigg) $$ \times (-1) =-1]$
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
difficult
q41
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The ratio in which the line $3x + 4y + 2 = 0$ divides the distance between the lines $3x + 4y + 5 = 0$ and $3x + 4y – 5 = 0$ is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q40
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. A line passes through (2, 2) and is perpendicular to the line $3x + y=3$. Its y - intercept is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q39
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. A point equidistant from the lines $4x + 3y + 10 = 0, 5x – 12y + 26 = 0$ and $7x+24y-50=0$ is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q38
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The point (4, 1) undergoes the following two successive transformations : \[\] (i) Reflection about the line $y=x$ \[\] (ii) Translation through a distance 2 units along the positive x-axis \[\] Then the final coordinates of the point are
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
difficult
q37
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. For specifying a straight line, how many geometrical parameters should be known ?
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q36
asked
Jul 6, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The coordinates of the foot of perpendiculars from the point (2, 3) on the line $y = 3x + 4 $ is given by
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q32
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The distance between the lines $ y = mx + c_1$ and $ y = mx + c_2$ is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
easy
q31
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The equations of the lines passing through the point (1, 0) and at a distance $ \large\frac{\sqrt 3 }{2}$ from the origin, are
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q30
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The equations of the lines which pass through the point (3, –2) and are inclined at $ 60^{\circ}$ to the line $3 x + y = 1$ is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q29
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The distance of the point of intersection of the lines 2x – 3y + 5 = 0 and 3x + 4y = 0 from the line 5x – 2y = 0 is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q28
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. If the line $ \large\frac{x}{a}$$+ \large\frac{y}{b}$$=1$ passes through the points (2, –3) and (4, –5), then (a, b ) is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q27
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
medium
q26
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The equation of the line passing through the point (1, 2) and perpendicular to the line $x+y+1 = 0 $ is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
easy
q25
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
easy
q24
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. Slope of a line which cuts off intercepts of equal lengths on the axes is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-question
sec-a
easy
q23
asked
Jul 3, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x - axis is $ \large\frac{3}{5}$, its equation is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-questions
sec-a
easy
q22
asked
Jul 2, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-questions
sec-a
medium
q35
asked
Jul 2, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options.Equation of the line passing through (1, 2) and parallel to the line y = 3x-1 is
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-questions
sec-a
medium
q34
asked
Jul 2, 2014
by
thanvigandhi_1
1
answer
Choose the correct answer from the given four options. If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be
cbse
math
class11
ch10
straight-lines
exemplar
objective-type-questions
sec-a
medium
q33
asked
Jul 2, 2014
by
thanvigandhi_1
1
answer
Find the equations of the lines through the point of intersection of the lines $x-y+1=0 $ and $ 2x-3y+5 = 0$ and whose distance from the point (3, 2) is $ \large\frac{7}{5}$
cbse
math
class11
ch10
straight-lines
exemplar
long-answer-type-question
sec-c
difficult
q18
asked
Jul 2, 2014
by
thanvigandhi_1
1
answer
Find the equation of the line which passes through the point (– 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point
cbse
math
class11
ch10
straight-lines
exemplar
long-answer-type-question
sec-b
difficult
q17
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point. \[\] [ Hint : $\large\frac{x}{a}$$ + \large\frac{y}{b}$$=1$ where $ \large\frac{1}{a}$$+\large\frac{1}{b}$ = constant = $ \large\frac{1}{k}$ (say ). This implies that $ \large\frac{k}{a}$$+\large\frac{k}{b}$$=1 \Rightarrow $ line passes through the fixed point (k, k).]
cbse
math
class11
ch10
straight-lines
exemplar
long-answer-type-question
sec-b
difficult
q16
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
In what direction should a line be drawn through the point (1, 2) so that its point of intersection with the line x + y = 4 is at a distance $ \large\frac{\sqrt 6}{3}$ from the given point
cbse
math
class11
ch10
straight-lines
exemplar
long-answer-type-question
sec-c
medium
q15
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P \[\] [Hint: Let the slope of the line be $m$. Then the equation of the line passing through the fixed point $P (x_1 , y_1 )$ is $y - y_1 = m (x - x_1 )$. Taking the algebraic sum of perpendicular distances equal to zero, we get $ y - 1 = m (x - 1). $ Thus $(x_1 , y_1 ) $ is $(1, 1)$.]
cbse
math
class11
ch10
straight-lines
exemplar
long-answer-type-question
sec-a
difficult
q14
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle \[\] [Hint: Find length of perpendicular (p) from (2, – 1) to the line and use $p = l \: \sin 60^{\circ}$, where $l$ is the length of side of the triangle]
cbse
math
class11
ch10
straight-lines
exemplar
long-answer-type-question
sec-b
medium
q13
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-b
difficult
q12
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of $120^{\circ}$ with the positive direction of $x$ - axis.\[\] [Hint: Use normal form, here $ \omega =30^{\circ}$.]
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-b
easy
q11
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
If the intercept of a line between the coordinate axes is divided by the point (–5 4) in the ratio 1 : 2, then find the equation of the line.
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-c
difficult
q10
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-b
difficult
q9
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-b
medium
q8
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
Find the equation of lines passing through (1, 2) and making angle $30^{\circ}$ with $y$ - axis.
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
seca
medium
q7
asked
Jul 1, 2014
by
thanvigandhi_1
1
answer
Show that the tangent of an angle between the lines $ \large\frac{x}{a}$$+\large\frac{y}{b}$$=1$ and $ \large\frac{x}{a}$$-\large\frac{y}{b}$$=1$ is $ \large\frac{2ab}{a^2-b^2}$
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-b
medium
q6
asked
Jun 30, 2014
by
thanvigandhi_1
1
answer
Find the points on the line x + y = 4 which lie at a unit distance from the line 4x + 3y = 10
cbse
math
class11
ch10
straight-lines
exemplar
short-answer-type-question
sec-b
medium
q5
asked
Jun 30, 2014
by
thanvigandhi_1
1
answer
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