Equation of Circles

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 from the equation of a circle?

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form: (x - h)² + (y - k)² = r².

Tags

CCSS.HSG.GPE.A.1

Front

What are congruent circles?

Back

Congruent circles are circles that have the same radius but may be located at different centers.

Tags

CCSS.8.G.A.2

Front

What is the center of a circle in the equation (x + 1)² + (y - 2)² = 16?

Back

The center of the circle is (-1, 2).

Tags

CCSS.HSG.GPE.A.1

Front

If the radius of a circle is 4, what is the equation of the circle centered at (0, 0)?

Back

The equation is x² + y² = 16.

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The diameter is 10, calculated as Diameter = 2 * Radius.

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 distance between the centers of two circles with equations (x - 1)² + (y - 2)² = 9 and (x + 3)² + (y + 4)² = 16?

Back

The distance is 5 units, calculated using the distance formula between the centers (1, 2) and (-3, -4).

Tags

CCSS.HSG.GPE.A.1

Front

What does the term 'concentric circles' mean?

Back

Concentric circles are circles that share the same center but have different radii.

Front

In the equation (x - 4)² + (y - 3)² = 25, what is the radius?

Back

The radius is 5, since √25 = 5.

Tags

CCSS.HSG.GPE.A.1