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

HARD

JEE Main

IMPORTANT

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If the straight line $2 x - 3 y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, β)$ , then $β$ equals :

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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 - 12th January 2019 Shift 2>Q 51

If a straight line passing through the point

P (- 3, 4)

is such that its intercepted portion between the coordinate axes is bisected at

P

, then its equation is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 12th January 2019 Shift 2>Q 52

If a circle of radius

R

passes through the origin

O

and intersects the coordinate axes at

A

and

B

, then the locus of the foot of perpendicular from

O

A B

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 12th January 2019 Shift 2>Q 53

The tangent to the curve

y = x^{2} - 5 x + 5

, parallel to the line

2 y = 4 x + 1

, also passes through the point :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 8th April 2018>Q 54

Let the orthocentre and centroid of a triangle be

A (- 3, 5)

and

B (3, 3)

respectively. If

C

is the circumcentre of this triangle, then the radius of the circle having line segment

A C

as diameter, is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 8th April 2018>Q 55

A straight line through a fixed point

(2, 3)

intersects the coordinate axes at distinct points

P

and

Q

. If

O

is the origin and the rectangle

O P R Q

is completed, then the locus of

R

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 15th April 2018>Q 56

In a triangle

A B C

, coordinates of

A

are

(1, 2)

and the equations of the medians through

B

and

C

are respectively,

x + y = 5

and

x = 4

. Then area of

Δ A B C

(in sq. units) is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 16th April 2018>Q 57

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

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:

If the straight line 2x-3y+17=0 is perpendicular to the line passing through the points 7,17 and 15, β, then β equals :

Important Questions on Point and Straight Line

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If the straight line $2 x - 3 y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, β)$ , then $β$ equals :