Recent questions and answers in Straight Lines

3x2−11xy+10y2−7x+13y+k=0 denotes a pair of straight lines find the value of k

answered Jul 1, 2015 by meena.p

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if the pair of straight lines x^2-2pxy-y^2=0 and x^2-2qxy-y^2=0 be such that each pair bisects the angles between the other pair prove that pq= -1

answered Feb 21, 2015 by sharmaaparna1

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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.

answered Jul 11, 2014 by thanvigandhi_1

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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

answered 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 value of the $ \lambda$, if the lines $(2x + 3y + 4) +\lambda (6x – y + 12) = 0 $ are

answered Jul 9, 2014 by thanvigandhi_1

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Match the question given under Column $C_1$ with their appropriate answer given under the Column $C_2$ for the following :

answered Jul 9, 2014 by thanvigandhi_1

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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).

answered 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

answered Jul 9, 2014 by thanvigandhi_1

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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)

answered 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 $y - 3 = (2 \pm \sqrt3 ) (x - 2)$.

answered Jul 9, 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$

answered 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 $

answered Jul 8, 2014 by thanvigandhi_1

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State whether the following statement is true or false and justify : The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear

answered 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 ____.

answered 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 $3x – 4y – 8 = 0$ .

answered Jul 8, 2014 by thanvigandhi_1

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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 _______.

answered Jul 8, 2014 by thanvigandhi_1

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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 _________.

answered 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 ____.

answered Jul 6, 2014 by thanvigandhi_1

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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]$

answered 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

answered 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

answered Jul 6, 2014 by thanvigandhi_1

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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

answered Jul 6, 2014 by thanvigandhi_1

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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

answered 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 ?

answered 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

answered Jul 6, 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

answered Jul 3, 2014 by thanvigandhi_1

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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

answered 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

answered 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

answered 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

answered Jul 3, 2014 by thanvigandhi_1

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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

answered Jul 3, 2014 by thanvigandhi_1

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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

answered Jul 3, 2014 by thanvigandhi_1

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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

answered Jul 3, 2014 by thanvigandhi_1

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Choose the correct answer from the given four options. Slope of a line which cuts off intercepts of equal lengths on the axes is

answered Jul 3, 2014 by thanvigandhi_1

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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

answered Jul 2, 2014 by thanvigandhi_1

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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

answered Jul 2, 2014 by thanvigandhi_1

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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

answered Jul 2, 2014 by thanvigandhi_1

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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

answered Jul 2, 2014 by thanvigandhi_1

1 answer