Question

Given the following equation of a circle in general form, find the equation in standard form by completing the square.

Answer 1

The standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have an equation that represents the circle:

4x² + 8x + 4y² + 32y +52 = 0

Divide by 4 on both the sides:

x² + 2x + y² + 8y + 13 = 0

x² + 2x + 1 - 1 + y² + 8y + 4² - 4² + 13 = 0

x² + 2x + 1 + y² + 8y + 4² - 1 - 16 + 13

(x + 1)² + (y + 4)² = 4

(x + 1)² + (y + 4)² = 2²

Thus, the standard form of the circle equation 4x² + 8x + 4y² + 32y +52 = 0 is (x + 1)² + (y + 4)² = 2²

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