Q. 19

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

The given line can be written as 4x + 3y -12 = 0

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

A = 4 , B = 3 and C = -12.

It is known that the perpendicular distance (d) of the line Ax + By + C = 0 from a point

(x1, y1) is given by

Therefore, if (0,b) is the point on the y – axis whose distance from line is 4 units, then,

⇒ 20 = |3b – 12|

⇒ 20 = (3b – 12)

⇒ 20 = (3b – 12) or 20 = -(3b-12)

⇒ 3b = 20 +12 or 3b = -20 +12

Therefore, the required points are

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