9.6 circle equations general form -> standard form

Front

What is the general form of a circle's equation?

Back

The general form of a circle's equation is x² + y² + Dx + Ey + F = 0, where D, E, and F are constants.

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x - a)² + (y - b)² = r², where (a, b) is the center and r is the radius.

Front

How do you convert from general form to standard form?

Back

To convert from general form to standard form, complete the square for the x and y terms.

Front

What value of c makes x² + 8x + c a perfect square trinomial?

Back

c = 16.

Front

What is the equation of a circle with center (a, b) and radius r?

Back

(x - a)² + (y - b)² = r².

Front

What value of c makes x² - 12x + c a perfect square trinomial?

Back

c = 36.

Front

What is the equation of a circle with center (4, 2) and radius 5?

Back

(x - 4)² + (y - 2)² = 25.

Front

Determine the equation of the circle in standard form: x² + y² + 4x + 6y - 36 = 0.

Back

(x + 2)² + (y + 3)² = 49.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as (x + a)².

Front

What is the center of a circle in standard form?

Back

The center of a circle in standard form (x - a)² + (y - b)² = r² is the point (a, b).