Recent questions tagged ch10

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)

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

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$

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 $

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

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 ____.

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 $3x – 4y – 8 = 0$ .

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 _______.

asked 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 _________.

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 ____.

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]$

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

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

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

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

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 ?

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

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

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

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

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

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

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

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

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

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

asked 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

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

asked 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

asked 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

asked Jul 2, 2014 by thanvigandhi_1

1 answer