Question

How do you graph `X^2+Y^2-10X-4Y+28=0`?

Answer 1

A circle with centre `(5,2)` and a radius of `1` unit.

Explanation:

Complete the square to identify relevant features in this graph.

`X^2 + Y^2 - 10X - 4Y + 28 = 0`
`X^2 - 2(5)X + 5^2 + Y^2 - 2(2)Y + 2^2 = 5^2 + 2^2 - 28`
`(X-5)^2+(Y-2)^2=1`

Thus, we see that this graph is a circle with centre `(5,2)` and a radius of `1` unit.