Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 20

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If the ratio of gradients of the lines represented by $a x^{2} + 2 h x y + b y^{2} = 0$ is $1 : 3$ , then the value of the ratio $h^{2} : a b$ is

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Important Questions on Pair of Straight Lines

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 21

The line joining origin and point of intersection of curves

a x^{2} + 2 h x y + b y^{2} + 2 g x = 0

and

a_{1} x^{2} + 2 h_{1} x y + b_{1} y^{2} + 2 g_{1} x = 0

will be mutually perpendicular if

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 22

A straight line passing through the point

(1, 0)

and not parallel to

x

-axis intersects the curve

2 x^{2} + 5 y^{2} - 7 x = 0

at two points

A

and

B

. The angle subtended by the line segment

A B

at the origin is

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 23

If the sum of the slopes of the lines given by

x^{2} - 2 c x y - 7 y^{2} = 0

is four times their product, then

c

has the value

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 24

The pair of straight lines passing through the point

(1, 2)

and perpendicular to the pair of straight lines

3 x^{2} - 8 x y + 5 y^{2} = 0

, is

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 25

Let the equation of the pair of lines,

y = p x

and

y = q x,

can be written as

(y - p x) (y - q x) = 0 .

Then the equation of the pair of the angle bisectors of the lines

x^{2} - 4 x y - 5 y^{2} = 0

is:

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 26

The point of intersection of lines represented by

x^{2} - y^{2} + x + 3 y - 2 = 0

is

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 27

If the lines represented by the equation

3 y^{2} - x^{2} + \sqrt{3} x - 3 = 0

are rotated about the point

(\sqrt{3}, 0)

through an angle of

15^{°},

one clockwise direction and other in anti-clockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

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Mathematics Crash Course MHT-CET>Chapter 6 - Pair of Straight Lines>Exercise 1>Q 28

The equation

x^{2} + k y^{2} + 4 x y = 0

represents two coincident lines, if

k =