Question

Given the following equation of a circle in general form, find the equation in standard form by completing the square. 2x²+12x+2y²+20y - 4 = 0

Answer 1

To convert the equation of a circle from general form to standard form by completing the square, follow these steps. In this case, the transformed equation in standard form is (x + 3)² + (y + 5)² = 20.

Step-by-step explanation:

To convert the equation of a circle from general form to standard form by completing the square, follow these steps:

1. Group the x terms and y terms together.
2. Move the constant term to the other side of the equation.
3. Complete the square for x by adding half the coefficient of x squared to both sides, then square the result.
4. Complete the square for y by adding half the coefficient of y squared to both sides, then square the result.
5. Write the equation in standard form by grouping the squared terms and moving the constant term to the other side.

In this case, the transformed equation in standard form is (x + 3)² + (y + 5)² = 20.