Equation of a circle

Question

Given the general equation of a circle is x² + y² + 2x - 4y - 4 = 0

Write the equation in the form of (x - h)² + (y - k)² = r²

Answer 1

x² + y² + 2x - 4y - 4 = 0

x² + y² + 2x - 4y = 4 move number to right side of equation

x² + 2x + y² - 4y = 4 re-organize terms so x and y terms together

x² + 2x + 1 + y² - 4y + 4 = 9 complete the square of x and y terms and add same amount to right side

(x+1)² + (y-2)² = 9 express as squares so in equation of circle form