Circle Equations and Degree Conversions

Front

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

Back

The standard form of a circle's equation 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 from the equation of a circle?

Back

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

Front

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

Back

The center of the circle is (-3, 4).

Front

If the radius of a circle is 5, what is the equation of the circle centered at (2, -1)?

Back

The equation of the circle is (x - 2)² + (y + 1)² = 25.

Front

Convert 180 degrees to radians.

Back

180 degrees is equal to π radians.

Front

What is the relationship between degrees and radians?

Back

Degrees and radians are two units for measuring angles; 180 degrees is equal to π radians.

Front

What is the radius of the circle given by the equation (x - 1)² + (y + 2)² = 49?

Back

The radius of the circle is 7.

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by 180/π.

Front

What is the center of the circle given by the equation (x - 5)² + (y + 3)² = 16?

Back

The center of the circle is (5, -3).

Front

Write the equation of a circle with center (0, 0) and radius 4.

Back

The equation of the circle is x² + y² = 16.