Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 18

EASY

JEE Main/Advance

IMPORTANT

Earn 100

A line having slope $' 1'$ is drawn from a point $A (- 3, 0)$ cuts a curve $y = x^{2} + x + 1$ at $P & Q .$ Find $ℓ (A P)$ $ℓ (A Q)$

Important Questions on Point and Straight Line

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 19

Find the direction in which a straight line must be drawn through the point

(- 1, 2)

so that its point of intersection with the line

x + y = 4

may be at a distance of

3

units from this point.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 20

Through the point

(3, 4)

are drawn two straight lines each inclined at

45 °

to the straight line

x - y = 2

. Find their equations and find also the area included by the three lines.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 21

Find the equation of a straight lines which passes through the point $(2, 1)$ and makes an angle of $\frac{π}{4}$ with the straight line $2 x + 3 y + 4 = 0$ .

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 22

From

(1, 4)

you travel

5 \sqrt{2}

units by making

135 °

angle with positive

x

-axis (anticlockwise) and then

4

units by making

120 °

angle with positive

x

-axis (clockwise) to reach

Q

. Find co-ordinates of point

Q

.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 23

The ends of the hypotenuse of a right angled triangle are

(6, 0)

and

(0, 6)

, then find the locus of third vertex of triangle.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 24

A point moves in the

x y

-plane such that the sum of its distances from two mutually perpendicular lines is always equal to

3,

then find the area enclosed by the locus of the point.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 25

One side of a rectangle lies along the line

4 x + 7 y + 5 = 0 .

Two of its vertices are

(- 3, 1)

and

(1, 1)

Then find the equations of other sides.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 26

Plot the region
(i)

6 x + 2 y \geq 31