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

HARD

JEE Main

IMPORTANT

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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 $x + 5 y = 0$ is

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Important Questions on Point and Straight Line

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 7th April 2013>Q 78

The

x -

coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as

(0, 1), (1, 1)

and

(1, 0)

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 7th April 2013>Q 79

The number of values of $k$ , for which the system of equations :

$(k + 1) x + 8 y = 4 k$

$k x + (k + 3) y = 3 k - 1$

has no solution, is :

If a line L is perpendicular to the line 5x-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+5y=0 is

Important Questions on Point and Straight Line

Learn and Prepare for any exam you want !

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 $x + 5 y = 0$ is