A circle C is tangent to the line y = -2, and also externally tangent to the circle x^2 + y^2 = 1. Given that the center of circle C is O = (16,a), what is the value of a?
+128475 Let the distance from the center of the circle to the line y = -2 be
sqrt [ ( a + 2)]^2 this is the radius of the circle
And the center of x^2 + y^2 =1 is (0, 0) and its radius = 1
And since circle C is tangent to the circle x^2 + y^2 =1
Then the distance from ( 16,a) to this center is 1 greater than the radius
So...we have this equation
sqrt [ (a + 2)^2 ]+ 1 = sqrt [16^2 + a^2 ]
(a + 2)+ 1 = sqrt (256 + a^2)
a + 3 = sqrt (256 + a^2) square both sides
a^2 + 6a + 9 = a^2 + 256 subtract a^2 from both sides
6a + 9 = 256
6a = 247
a = 247 / 6
