Question

What are the points on the y -axis whose distance from the line is 4 units.

Answer 1

The equation of line is x 3 + y 4 =1. The distance of line is 4 units with points on y axis.

Let the point on y axis be ( 0,b ) whose distance from the line is 4 units.

The given line can be rewritten as,

4x+3y−12=0(1)

On comparing equation (1) with the general equation of line Ax+By+C=0, we obtain,

A=4,B=3, and C=−12.(2)

The formula for the perpendicular distance of the line Ax+By+C=0 from a point ( x 1 , y 1 ) is given by,

d= | A x 1 +B y 1 +C | A 2 + B 2 (3)

Substitute the values of d as 4, ( x 1 , y 1 ) as ( 0,b ), and the values of A, B and C from equation (2) in equation (3).

4= | 4×0+3×b−12 | 4 2 + 3 2 4= | 3b−12 | 5 5×4=| 3b−12 | 20=| 3b−12 |

If mod opens with positive sign.

20=( 3b−12 ) 20=3b−12 3b=32 b= 32 3

If mod opens with negative sign.

20=−( 3b−12 ) 20=−3b+12 −3b=8 b=− 8 3

Thus, the points on y axis are ( 0, 32 3 ) and ( 0,− 8 3 ).