Question

What are the equations of the circles tangent to the x-axis, of radius 4 and whose center is at (-2,y)

Please help, how do I solve this problem?

Answer 1

Since (-2,0) must be on the circle , (it is tangent to that point)
y must be either 4 or -4

first case: y = 4
centre is (-2,4) radius is 4

equation: (x+2)^2 + (y-4)^2 = 16

you try the other circle with centre (-2,-4)

Answer 2

-2,-4