Conics- Circles

Front

What is the standard equation of a circle?

Back

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

Front

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

Back

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

Front

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

Back

The radius is √16 = 4 units.

Front

If a circle has a center at (0, 0) and a radius of 5, what is its equation?

Back

The equation is x² + y² = 25.

Front

What are the coordinates of the center of the circle given by the equation (x + 4)² + (y - 1)² = 36?

Back

The center is (-4, 1).

Front

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

Back

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

Front

Write the equation of a circle with center (2, -3) and radius 6.

Back

The equation is (x - 2)² + (y + 3)² = 36.

Front

What is the distance between the center and a point on the circle?

Back

The distance is equal to the radius of the circle.

Front

What is the equation of a circle with center (-1, 4) and radius 2?

Back

The equation is (x + 1)² + (y - 4)² = 4.

Front

If the equation of a circle is (x - 5)² + (y + 3)² = 49, what is the radius?

Back

The radius is √49 = 7 units.