Question

How do you solve `2( x + 2) ^ { 2} + 2( y - 3) ^ { 2} = 10`?

Answer 1

It has an infinite number of solutions; it is a circle with its center located at `(-2,3)` and a `"radius "=sqrt5`. Every point on the circle is a solution.

Explanation:

Given: `2( x + 2)^2 + 2( y - 3)^2 = 10`

Divide both sides of the equation by 2:

`( x + 2)^2 + ( y - 3)^2 = 5`

The standard form is `(x - h)^2 + (y-k)^2 = r^2`, therefore, we write the +2 as a negative number:

`( x - (-2))^2 + ( y - 3)^2 = 5`

And we write the 5 as the square of a square root:

`( x - (-2))^2 + ( y - 3)^2 = (sqrt(5))^2`

This allows us to easily observe that the center is `(-2,3)` and the radius is `sqrt5`