Find if the distance between the point (2, y) and the line 3x-4y+5 = 0 is 12 units. Find y

The distance between a point (x1, y1) and a line ax + by +
c = 0 is given by: |a*x1 + b*y1 + c|/sqrt (a^2 +
b^2)

Substituting the values we have
here

D = |a*x1 + b*y1 + c|/sqrt (a^2 +
b^2)

=> |3*2 - 4*y + 5|/sqrt (3^2 +
4^2)

=> |6 - 4y + 5|/ sqrt
25

Now D = 12

=> 60 =
|11 - 4y|

=> 11 -4y = 60 and 11 - 4y =
-60

=> 4y = -49 and -4y =
-71

=> y = -49/4 and y = 71/
4

The values of y are y = -49/4 and y = 71/
4