Using the following equation, find the center and radius: x² + 2x + y² + 4y = 20

Solution:

Given equation x² + 2x + y² + 4y = 20

We know that the equation of circle with centre (h, k) and radius r is given by (x - h)² +(y - k)² = r²

In order to bring the given equation in standard form, let us complete the square and make two perfect square trinomials on LHS.

(x² + 2x )+ (y² + 4y)= 20

(x² + 2x + (-1)² )+ (y² + 4y + (-2)²) = 20+ 1+ 4

Since a² + 2ab + b²= (a + b)²

(x + 1)² + (y + 2)² = 25

By comparing, we get centre (h, k) as (-1, -2) and radius r as 5.

Using the following equation, find the center and radius: x² + 2x + y² + 4y = 20

Summary:

Using the following equation, x² + 2x + y² + 4y = 20 we get the centre as (-1, -2) and radius r as 5.