Equations of Circles

Front

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

Back

(x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

Front

What does the variable 'r' represent in the equation of a circle?

Back

The radius of the circle.

Front

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

Back

The center (h,k) can be found from the equation (x-h)² + (y-k)² = r².

Front

What is the radius of the circle with the equation (x+1)² + (y-2)² = 25?

Back

5 (since r² = 25, r = √25 = 5).

Front

What is the center of the circle given by the equation (x-4)² + (y+3)² = 36?

Back

(4, -3).

Front

If the radius of a circle is 7, what is the equation of the circle in standard form?

Back

(x-h)² + (y-k)² = 49, where (h,k) is the center.

Front

What is the distance formula used for in relation to circles?

Back

To find the distance between the center of the circle and any point on the circle.

Front

What does the term 'conic sections' refer to?

Back

Shapes created by intersecting a plane with a cone, including circles, ellipses, parabolas, and hyperbolas.

Front

How can you determine if a point lies inside, on, or outside a circle?

Back

By comparing the distance from the center to the point with the radius.

Front

What is the equation of a circle with center at (0,0) and radius 3?

Back

x² + y² = 9.