SOLUTION: find the equation of a circle with center at (-4,2) and tangent to the line 2x-y+2=0

Algebra ->  Circles -> SOLUTION: find the equation of a circle with center at (-4,2) and tangent to the line 2x-y+2=0      Log On


   

Question 938729: find the equation of a circle with center at (-4,2) and tangent to the line 2x-y+2=0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Circle: %28x%2B4%29%5E2+%2B+%28y-2%29%5E2+=+r%5E2
tangent to...
y = 2x + 2
...
Line perpendicular thru C(-4,2)
y - 2 = (-1/2)(x + 4)
y = (-1/2)x
...
(-1/2)x = 2x + 2
-2 = (5/2)x
(-4/5) = x and y = 2/5 %28-1%2F2%29%28-4%2F5%29
...
C(-4,2)
(-4/5, 2/5)
r^2 = +%28x%5B1%5D-x%5B2%5D%29%5E2%2B+%28y%5B1%5D-y%5B2%5D%29%5E2++
...
r^2 = %28-16%2F5%29%5E2+%2B+%288%2F5%29%5E2 = 320/25
%28x%2B4%29%5E2+%2B+%28y-2%29%5E2+=+r%5E2