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.
2 answers
find the distance from the center of the circle to the line. Use that for the radius of the circle.
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
(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
1 answer