HARD

JEE Main/Advance

IMPORTANT

Earn 100

If the straight lines joining the origin and the points of intersection of the curve $5 x^{2} + 12 x y - 6 y^{2} + 4 x - 2 y + 3 = 0$ and $x + k y - 1 = 0$ are equally inclined to the $x$ -axis, then find the value of $|k| .$

Important Questions on Point and Straight Line

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 30

If the points of intersection of curves

C_{1} = 4 y^{2} - λ x^{2} - 2 x y - 9 x + 3

and

C_{2} = 2 x^{2} + 3 y^{2} - 4 x y + 3 x - 1

subtends a right angle at origin, then find the the value of

λ .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 31

A parallelogram is formed by the lines

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

and the lines through

(p, q)

parallel to them and the equation of the diagonal of the parallelogram which doesn't pass through origin is

(λ x - p) (a p + h q) + (μ y - q) (h p + b q) = 0,

then find the value of

λ^{3} + μ^{3} .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 32

The equation

9 x^{3} + 9 x^{2} y - 45 x^{2} = 4 y^{3} + 4 x y^{2} - 20 y^{2}

represents

3

straight lines, two of which passes through origin. Then find the area of the triangle formed by these lines

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 33

Point

P (2, 3)

lies on the line

4 x + 3 y = 17 .

Then find the co-ordinates of points farthest from the line which are at

5

units distance from the

P .

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 34

Find the equation of the line passing through the point

(2, 3)

making intercept of length

2

units between the lines

y + 2 x = 3

y + 2 x = 5 .

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 35

In a triangle

A B C,

co-ordinates of

A

are

(1, 2)

and the equations to the medians through

B

and

C

are

x + y = 5

and

x = 4

respectively. Then, the co-ordinates of

B

and

C

will be

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 36

A

is a point on either of two rays

y + \sqrt{3} | x | = 2

at a distance of

\frac{4}{\sqrt{3}}

units from their point of intersection. The co-ordinates of the foot of perpendicular from

A

on the bisector of the angle between them is/are

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 37

If one side of a square is parallel to

3 x - 4 y = 0 &

its area being

16

while centre being

(1, 1),

then find the equation of the sides of the parallelogram.

If the straight lines joining the origin and the points of intersection of the curve 5x2+12xy-6y2+4x-2y+3=0 and x+ky-1=0 are equally inclined to the x -axis, then find the value of k.

Important Questions on Point and Straight Line

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If the straight lines joining the origin and the points of intersection of the curve $5 x^{2} + 12 x y - 6 y^{2} + 4 x - 2 y + 3 = 0$ and $x + k y - 1 = 0$ are equally inclined to the $x$ -axis, then find the value of $|k| .$