The locus of the point of intersection of the lines 2 x - y + 4 2 k = 0 and 2 k x + k y - 4 2 = 0 ( k is any non-zero real parameter) is

a hyperbola with length of its transverse axis 8 2

an ellipse whose eccentricity is 1 3

a hyperbola whose eccentricity is 3

an ellipse with length of its major axis 8 2

The locus of the point of intersection of the lines 2 x - y + 4 2 k = 0 and 2 k x + k y - 4 2 = 0 ( k is any non-zero real parameter) is

a hyperbola with length of its transverse axis 8 2

If a variable line drawn through the intersection of the lines x 3 + y 4 = 1 and x 4 + y 3 = 1 , meets the coordinate axes at A and B , A ≠ B , then the locus of the midpoint of AB is:

14 x + y 2 - 97 x + y + 168 = 0

MEDIUM

JEE Main

IMPORTANT

Earn 100

The locus of the point of intersection of the lines $\sqrt{2} x - y + 4 \sqrt{2} k = 0$ and $\sqrt{2} k x + k y - 4 \sqrt{2} = 0$ ( $k$ is any non-zero real parameter) is

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Important Questions on Point and Straight Line

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 2nd April 2017>Q 58

Let

k

be an integer such that the triangle with vertices

(k, - 3 k), (5, k)

and

(- k, 2)

has area

28

sq. units. Then the orthocenter of this triangle is at the point:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 9th April 2017>Q 59

A square, of each side

2

, lies above the

x

-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle

30 °

with the positive direction of the

x

-axis , then the sum of the

x

-coordinates of the vertices of the square is

:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 9th April 2016>Q 60

If a variable line drawn through the intersection of the lines

\frac{x}{3} + \frac{y}{4} = 1

and

\frac{x}{4} + \frac{y}{3} = 1

, meets the coordinate axes at

A

and

B

(A \neq B),

then the locus of the midpoint of

AB

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 9th April 2016>Q 61

The point

(2, 1)

is translated parallel to the line

L : x - y = 4

2 \sqrt{3}

units. If the new point

Q

lies in the third quadrant, then the equation of the line passing through

Q

and perpendicular to

L

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 3rd April 2016>Q 62

Two sides of a rhombus are along the lines,

x - y + 1 = 0

and

7 x - y - 5 = 0

. If its diagonals intersect at

(- 1, - 2)

, then which one of the following is a vertex of this rhombus ?

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 10th April 2016>Q 63

A straight line through origin

O

meets the lines

3 y = 10 - 4 x

and

8 x + 6 y + 5 = 0

at points

A

and

B

respectively. Then,

O

divides the segment

A B

in the ratio

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 10th April 2016>Q 64

A ray of light is incident along a line which meets another line

7 x - y + 1 = 0

at the point

(0, 1)

. The ray is then reflected from this point along the line

y + 2 x = 1

. Then the equation of the line of incidence of the ray of light is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 10th April 2015>Q 65

If the points

(1, 1, λ) & (- 3, 0, 1)

, are equidistant from the plane,

3 x + 4 y - 12 z + 13 = 0,

then

λ

satisfies the equation:

The locus of the point of intersection of the lines 2x-y+42k=0 and 2kx+ky-42=0 (k is any non-zero real parameter) is

Important Questions on Point and Straight Line

Learn and Prepare for any exam you want !

The locus of the point of intersection of the lines $\sqrt{2} x - y + 4 \sqrt{2} k = 0$ and $\sqrt{2} k x + k y - 4 \sqrt{2} = 0$ ( $k$ is any non-zero real parameter) is