Let a and b be any two numbers satisfying 1 a 2 + 1 b 2 = 1 4 . Then, the foot of perpendicular from the origin on the variable line x a + y b = 1 lies on :

A hyperbola with each semi-axis = 2 .

A hyperbola with each semi-axis = 2

MEDIUM

JEE Main

IMPORTANT

Earn 100

Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a

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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 - 11th April 2015>Q 70

A straight line

L

through the point

(3, - 2)

is inclined at an angle of

60 °

to the line

\sqrt{3} x + y = 1 .

L

also intersects the

X

-axis, then the equation of

L

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 19th April 2014>Q 71

If a line

L

is perpendicular to the line

5 x - y = 1,

and the area of the triangle formed by the line

L

and the coordinate axes is

5

sq units, then the distance of the line

L

from the line

x + 5 y = 0

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 19th April 2014>Q 72

The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points

(a^{2} + 1, a^{2} + 1)

and

(2 a, - 2 a), a \neq0

. Then for any

a,

the orthocentre of this triangle lies on the line

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 9th April 2014>Q 73

Given three points

P, Q, R

with

P (5, 3)

and

R

lies on the

x -

axis. If the equation of

R Q

x - 2 y = 2

and

P Q

is parallel to the

x -

axis, then the centroid of

Δ P Q R

lies on the line

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 9th April 2014>Q 74

Let

a

and

b

be any two numbers satisfying

\frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{4} .

Then, the foot of perpendicular from the origin on the variable line

\frac{x}{a} + \frac{y}{b} = 1

lies on :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 6th April 2014>Q 75

Let

P S

be the median of the triangle with vertices

P (2, 2), Q (6, - 1)

and

R (7, 3)

. The equation of the line passing through

(1, - 1)

and parallel to

P S

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 6th April 2014>Q 76

Let

a, b, c

and

d

be non-zero numbers. If the point of intersection of the lines

4 a x + 2 a y + c = 0 & 5 b x + 2 b y + d = 0

lies in the fourth quadrant and is equidistant from the two axes then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 7th April 2013>Q 77

A ray of light along

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

gets reflected upon reaching

X -

axis, the equation of the reflected ray is

Locus of the image of the point ( 2,3 ) in the line 2 x - 3 y + 4 + k x - 2 y + 3 = 0 , k ∈ R , is a

Important Questions on Point and Straight Line

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Locus of the image of the point $(2, 3)$ in the line $(2 x - 3 y + 4) + k (x - 2 y + 3) = 0, k \in R,$ is a