Question

Complete the square to rewrite the following equation. Identify the center and radius of the circle. You must show all work and calculations to receive credit.
x2 + 4x + y2 − 6y = −4

Answer 1

The Center of the given circle is at (-2, 3) and radius of circle is 3.

How to use the method of completing the square?

The general form of equation of a circle is;

(x - h)² + (y - k)² = r²

Where h and k are the center and r is the radius of the circle;

The given equation of the circle is;

x² +  4x +  y² - 6y = -4

Add 4 to both sides to get;

x² +  4x +  4 + y² - 6y = 0

Factoring the x part gives;

(x + 2)² + y² - 6y = 0

Add 9 to both sides to get;

(x + 2)² + y² - 6y = 0

Factoring the y part gives;

(x + 2)² + (y - 3)² = 9

⇒ (x + 2)² + (y - 3)² = 3²

Comparing the above with the general circle equation form gives;

(h, k) = (-2, 3) and r = 3

Thus;

Center of circle is at (-2, 3) and radius of circle is 3.

Read more about Completing the square at; brainly.com/question/3350489

#SPJ1