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

HARD

JEE Main

IMPORTANT

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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 :

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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 - 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

is

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)

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 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 :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 24 June 2022 Shift 1>Q 80

Let

A (\frac{3}{\sqrt{a}}, \sqrt{a}), a > 0

, be a fixed point in the

x y

-plane. The image of

A

in

y

-axis be

B

and the image of

B

in

x

-axis be

C

. If

D (3 \cos θ, a \sin θ)

, is a point in the fourth quadrant such that the maximum area of

∆ A C D

is

12

square units, then

a

is equal to _____

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 24 June 2022 Shift 2>Q 81

Let the area of the triangle with vertices

A (1, α), B (α, 0)

and

C (0, α)

be

4

sq. units. If the points

(α, - α), (- α, α)

and

(α^{2}, β)

are collinear, then

β

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 25 June 2022 Shift 2>Q 82

A circle touches both the

y

-axis and the line

x + y = 0

. Then the locus of its center is