The parabola y = x^2 is tangent to a circle at (2,4). The circle passes through the point (0,7). Find the center of the circle.
+128475 The center of the circle will be on the y axis.....let's call this point (0 , a)
The distance from this point to (2,4) and to (0,7) will be the radius
So we can equate distances (using the square of the distance formula on both sides of the equation )
( 0 - 0 )^2 + ( 7 -a)^2 = ( 2- 0)^2 + ( 4 - a)^2 simplify
a2 - 14a + 49 = 4 + a^2 - 8a + 16
-14a + 49 = -8a + 20
49 -20 = 14a - 8a
29 = 6a
a = 29/6
So the center is ( 0, 29/6) and the radius = 7 - 29/6 = 42/6 - 29/6 = 13/6
The radius = 7 - 29/6 = 42/6 - 29/6 = 13/6
