Question

when you are given an equation that is not in standard for and asked to write it in standard form for a circle, what do you do?

Answer 1

To write an equation in standard form for a circle, identify the equation for a circle, manipulate the given equation to match the standard form, and identify the values of the center and radius.

Step-by-step explanation:

When given an equation that is not in standard form and asked to write it in standard form for a circle, you need to follow these steps:

1. Identify the equation that represents a circle. The general equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
2. Manipulate the given equation to match the general form. You may need to expand squares, combine like terms, or rearrange the equation.
3. Once the equation is in the standard form, compare it to the general equation and identify the values of h, k, and r.

For example, if you are given the equation x^2 + y^2 + 4x - 6y + 9 = 0, you can rearrange it to get (x + 2)^2 + (y - 3)^2 = 4. So the center is (-2, 3) and the radius is 2.