# Re write an equation of a circle in standard form

Take the x-term coefficient, multiply it by one-half, square it, and then add this to both sides of the equation, as shown. The center is -4,5 and the radius is.

Is this equation even a circle? You'll need space inside your groupings, because this is where you'll add the squaring term.

We will be creating two perfect square trinomials within the equation. This equation is a circle.

Derivation of the Circle Formula With a little help from the Pythagorean Theorem, we can easily verify the circle equation formulas. Notice that in this form, we can clearly see that the equation of a circle has both x2 and y2 terms and these terms have the same coefficient usually 1, but not always.

## Equation of a circle explained

Circle with Center at Point h, k Known as "center-radius form" or "standard form". To accomplish this conversion, you will need to "complete the square" on the equation. Do not estimate round an answer unless told to do so, or unless working in a real world measurement situation. Also, if you get in the habit of always working the exercises in the same manner, you are more likely to remember the procedure on tests. Do the same with the y-term coefficient. Also, remember that the formula says "r2", not "r", so the radius in this case is sqrt 5 , not 5. This equation is a circle. We will, however, have to deal with the coefficients of 2 before we complete the square.

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