Question

What is the equation of the circle with a center at `(7 ,1 )` and a radius of `2`?

Answer 1

`y =+-` `\sqrt(4-(x²-14x+49))+1`.

Explanation:

For a circle with center `(h,k)` and radius `r`:

`(x-h)^2+(y-k)^2 = r^2`.

So

`(x-7)^2+(y-1)^2 = 4`

`x^2-14x+49+y^2-2y+1 = 4`

`(y-1)^2 = 4-(x^2-14x+49)`

`(y-1) =\sqrt{4-(x^2-14x+49)}`

graph{(x-7)^2+(y-1)^2 = 4 [-1.42, 11.064, -2.296, 3.944]}