Question

Find the equation of the circle which is concentric with the circle x^2+y^2+3y-8y+16=0 and tangent to the line 4x+3y-12=0. Show your solution.

Answer 1

find the distance from the center of the circle to the line. Use that for the radius of the circle.

Answer 2

x^2+y^2+3x-8y+16=0 is the circle

(x + 3/2)^2 + (y-4)^2 = 9/4

So, the center of the circle is at (-3/2,4)

The distance to the line 4x+3y-12=0 is thus

|4(-3/2) + 3(4) - 12|/√(4^2+3^2) = 6/5

So, the desired circle is

(x + 3/2)^2 + (y-4)^2 = 36/25