Circle -- coordinate geometry

A circle passes through the points (2,0) and (8,0) and has the y axis as a tangent. Find the two possible equations. 

Let the coordinates of the centre of circle be (x,y)

Let R be the radius of the circle.

So, R² = (x – 2)² + (y – 0)² = (x – 8)² + (y – 0)²

Or, x² – 4x + 4 + y² = x² – 16x + 64 + y²

Or, 12x = 60

Or, x = 5.

Since the normal to the tangent (x = 0) is parallel to the X Axis, so R = x – 0 = 5 – 0 = 5

Finding y with the help of coordinate (2,0), (5,y) and R = 5

5² = (5 – 2)² + (y – 0)²

Or, y = ±4

So, forming equation of circle with y = +4 and y = -4

We get

(x – 5)² + (y – 4)² = 25 for y = +4

(x – 5)² + (y + 4)² = 25 for y = - 4