Circle Equations Review

Front

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

Back

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

Tags

CCSS.HSG.GPE.A.1

Front

How do you find the center of a circle from its equation?

Back

To find the center of a circle from its equation in standard form (x - h)² + (y - k)² = r², identify the values of h and k.

Tags

CCSS.HSG.GPE.A.1

Front

What is the radius of a circle in the equation (x - 3)² + (y + 2)² = 16?

Back

The radius is r = √16 = 4.

Tags

CCSS.HSG.GPE.A.1

Front

Convert the general form of a circle's equation x² + y² + 6x - 4y - 12 = 0 to standard form.

Back

The standard form is (x + 3)² + (y - 2)² = 25.

Tags

CCSS.HSG.GPE.A.1

Front

What is the center of the circle in the equation (x + 1)² + (y - 4)² = 9?

Back

The center is (-1, 4).

Tags

CCSS.HSG.GPE.A.1

Front

How do you determine the radius from the equation (x - 5)² + (y + 1)² = 36?

Back

The radius is r = √36 = 6.

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The general form is x² + y² + Dx + Ey + F = 0.

Tags

CCSS.HSG.GPE.A.1

Front

Find the center and radius of the circle given by the equation x² + y² - 8x + 6y + 12 = 0.

Back

Center: (4, -3), Radius: 5.

Tags

CCSS.HSG.GPE.A.1

Front

What does the term 'completing the square' refer to in the context of circle equations?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, which helps in finding the center and radius of a circle.

Tags

CCSS.HSG.GPE.A.1

Front

If a circle has a center at (2, -1) and passes through the point (5, 2), what is its equation?

Back

The equation is (x - 2)² + (y + 1)² = 18.

Tags

CCSS.HSG.GPE.A.1