A circle Gamma is tangent to the line y = -2 and also externally tangential to the circle x^2 + y^2 = 1. Given that the center of Gamma is O = (16,a), what is the value of a?
+128474 The center of the x^2 + y^2 + 1 = (0,0)
The radius of Gamma = ( a + 2) = r
The distance from (16,a) to (0, 0) = (r + 1) = ( a + 2 + 1) = (a + 3)
16^2 + a^2 = ( a+ 2 + 1)^2
256 + a^2 = (a + 3)^2
256 + a^2 = a^2 + 6a + 9
6a = 247
a = 247/6
See the graph here : https://www.desmos.com/calculator/l9klwgdmus
