EASY

JEE Advanced

IMPORTANT

Earn 100

Find the coordinates of the point of intersection of the straight lines whose equations are $y = m_{1} x + \frac{a}{m_{1}}$ and $y = m_{2} x + \frac{a}{m_{2}}$ .

Important Questions on The Straight Line, Rectangular Coordinates

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 4

Find the coordinates of the point of intersection of the straight lines whose equations are

x \cos ϕ_{1} + y \sin ϕ_{1} = a

and

x \cos ϕ_{2} + y \sin ϕ_{2} = a

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 5

Two straight lines cut the axis of

x

at distances

a

and

- a

and the axis of

y

at distances

b

and

b^{'}

respectively; find the coordinates of their point of intersection.

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 6

Find the distance of the point of intersection of the two straight lines

2 x - 3 y + 5 = 0

and

3 x + 4 y = 0

from the straight line

5 x - 2 y = 0

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 7

Show that the perpendicular from the origin upon the straight line joining the points

(a \cos α, a \sin α)

and

y = \frac{c_{1} a_{2} - c_{2} a_{1}}{a_{1} b_{2} - a_{2} b_{1}}

bisects the distance between them.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 8

Find the equations of the two straight lines drawn through the point

(0, a)

on which the perpendiculars let fall from the point

(2 a, 2 a)

are each of length

a

.
Prove also that the equation of the straight line joining the feet of these perpendiculars is

y + 2 x = 5 a

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 9

Find the point of intersection and the angle between the two lines

A x + B y = A + B

and

A (x - y) + B (x + y) = 2 B

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 10

Find the coordinates of the point in which the line

2 y - 3 x + 7 = 0

meets the line joining the two points

(6, - 2)

and

(- 8, 7)

. Also find the angle between them.

HARD

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 11

Find the coordinates of the feet of the perpendiculars drawn from the point

(5, 0)

upon the sides of the triangle formed by joining the three points

(4, 3), (- 4, 3)

and

(0, - 5);

also prove that the points so determined lie on a straight line.

Find the coordinates of the point of intersection of the straight lines whose equations are y=m1x+am1 and y=m2x+am2.

Important Questions on The Straight Line, Rectangular Coordinates

Learn and Prepare for any exam you want !

Find the coordinates of the point of intersection of the straight lines whose equations are $y = m_{1} x + \frac{a}{m_{1}}$ and $y = m_{2} x + \frac{a}{m_{2}}$ .