MEDIUM

JEE Advanced

IMPORTANT

Earn 100

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 $5 x - 2 y = 0$ .

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 7

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

(a \cos α, a \sin α)

and

(a \cos β, a \sin β)

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.

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 12

Find the coordinates of the point of intersection of the straight lines

2 x - 3 y = 1

and

5 y - x = 3

and also determine the angle at which they cut each other.

MEDIUM

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 13

Find the angle between the two lines

3 x + y + 12 = 0

and

x + 2 y - 1 = 0 .

Also find the coordinates of their point of intersection and the equations of lines drawn perpendicular to them from the point

(3, - 2) .

EASY

JEE Advanced

IMPORTANT

The Elements of COORDINATE GEOMETRY Part 1 Cartesian Coordinates>Chapter 3 - The Straight Line, Rectangular Coordinates>EXAMPLES VIII>Q 14

Prove that the points whose coordinates are respectively

(5, 1), (1, - 1)

and

(11, 4)

lie on a straight line, and find its intercepts on the axes.

Find the distance of the point of intersection of the two straight lines 2x-3y+5=0 and 3x+4y=0 from the straight line 5x-2y=0.

Important Questions on The Straight Line, Rectangular Coordinates

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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 $5 x - 2 y = 0$ .