Equations of Circles Review

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.

Front

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

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.

Front

What is the center of the circle in the equation (x-1)² + (y+2)² = 9?

Back

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

Front

In the equation (x+4)² + (y-5)² = 25, what is the radius?

Back

The radius of the circle is 5.

Front

What does the equation x² + y² = 16 represent?

Back

This represents a circle centered at (0, 0) with a radius of 4.

Front

How do you convert the equation (x-3)² + (y+1)² = 16 into standard form?

Back

The equation is already in standard form: (x-3)² + (y+1)² = 4².

Front

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

Back

The equation is x² + y² = 9.

Front

In the equation (x+2)² + (y-3)² = 36, what is the center?

Back

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

Front

What is the radius of the circle represented by the equation (x-5)² + (y+2)² = 49?

Back

The radius of the circle is 7.

Front

How do you determine if a point (x, y) lies inside a circle?

Back

Substitute (x, y) into the circle's equation. If the left side is less than the right side, the point lies inside the circle.