Two identical circles touch at the point P(9,3)
one of the circles has equation x^2 + y^2 - 10x - 4y +12 = 0
find the equation of the other circle
+36916 Lets figure out the standard equation for a circle by completing the square
x^2-10x+25 + y^2-4x+4 = -12 +25 + 4
9x-5)^2 + (y-2)^2 = 17 center is h, k = 5,2
We want a straight line frome center through 9,3 to new center (so the circles will be tangent at 9,3)
5,2 to 9, 3 is a change of 4,1 add that to 9, 3 to get 13,4
SO the identical tangent circle is
(x-13)^2 + (y-4)^2 = 17
+36916 Lets figure out the standard equation for a circle by completing the square
x^2-10x+25 + y^2-4x+4 = -12 +25 + 4
9x-5)^2 + (y-2)^2 = 17 center is h, k = 5,2
We want a straight line frome center through 9,3 to new center (so the circles will be tangent at 9,3)
5,2 to 9, 3 is a change of 4,1 add that to 9, 3 to get 13,4
SO the identical tangent circle is
(x-13)^2 + (y-4)^2 = 17
