Equations of a Circle

Front

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

Back

The standard form of the equation of a circle 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 general form (Ax² + Ay² + Bx + Cy + D = 0), rewrite it in standard form and identify (h, k) from (x - h)² + (y - k)² = r².

Tags

CCSS.HSG.GPE.A.1

Front

What is the radius of a circle in standard form?

Back

In the standard form (x - h)² + (y - k)² = r², the radius r is the square root of the number on the right side of the equation.

Tags

CCSS.HSG.GPE.A.1

Front

Convert the equation x² + y² - 4x + 6y - 12 = 0 to standard form.

Back

(x - 2)² + (y + 3)² = 25.

Tags

CCSS.HSG.GPE.A.1

Front

What does the term 'completing the square' mean in the context of circles?

Back

Completing the square is a method used to rewrite a quadratic equation in the form of (x - h)² + (y - k)² = r² by rearranging and adjusting the equation.

Tags

CCSS.HSG.GPE.A.1

Front

What is the significance of the center of a circle?

Back

The center of a circle is the point from which all points on the circle are equidistant, and it is represented as (h, k) in the standard form.

Tags

CCSS.HSG.GPE.A.1

Front

How do you determine the radius from the equation of a circle?

Back

The radius can be determined from the standard form (x - h)² + (y - k)² = r² by taking the square root of r².

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The general form of the equation of a circle is x² + y² + Dx + Ey + F = 0.

Tags

CCSS.HSG.GPE.A.1

Front

How do you convert from general form to standard form?

Back

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

Tags

CCSS.HSG.GPE.A.1

Front

What is the center of the circle given by the equation x² + y² + 2x - 4y - 8 = 0?

Back

The center is (-1, 2).

Tags

CCSS.HSG.GPE.A.1