Circles and Parabolas

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 radius of a circle from its equation?

Back

To find the radius from the equation in standard form (x - h)² + (y - k)² = r², take the square root of r².

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The center of the circle is (3, -2).

Tags

CCSS.HSG.GPE.A.1

Front

What is the diameter of a circle if the radius is 5?

Back

The diameter is 2 times the radius, so the diameter is 10.

Tags

CCSS.7.G.B.4

Front

How do you convert the general form of a circle's equation to standard form?

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Tags

CCSS.HSG.GPE.A.1

Front

What is the relationship between the radius and diameter of a circle?

Back

The diameter is twice the radius (D = 2r).

Tags

CCSS.7.G.B.4

Front

What is the equation of a circle with center (0, 0) and radius 4?

Back

The equation is x² + y² = 16.

Tags

CCSS.HSG.GPE.A.1

Front

In the equation (x - 1)² + (y + 3)² = 25, what is the radius?

Back

The radius is 5.

Tags

CCSS.HSG.GPE.A.1

Front

What does the term 'completing the square' mean in relation to circles?

Back

Completing the square is a method used to rewrite a quadratic equation in standard form, which helps identify the center and radius of a circle.

Tags

CCSS.HSG.GPE.A.1

Front

What is the center of the circle given by the equation x² + y² - 6x + 8y = 0?

Back

The center is (3, -4).

Tags

CCSS.HSG.GPE.A.1