Circle Equations

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

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

Back

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

Front

What is the radius of the circle in the equation (x + 1)² + (y - 4)² = 25?

Back

The radius of the circle is 5.

Front

How do you find the center of a circle given its equation in standard form?

Back

To find the center, identify the values of h and k from the equation (x - h)² + (y - k)² = r².

Front

What is the radius of a circle with the equation x² + y² = 36?

Back

The radius is 6.

Front

Write the equation of a circle with center (2, -3) and radius 4.

Back

The equation is (x - 2)² + (y + 3)² = 16.

Front

What does the term 'h' represent in the standard equation of a circle?

Back

The term 'h' represents the x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the standard equation of a circle?

Back

The term 'k' represents the y-coordinate of the center of the circle.

Front

If a circle has a center at (0, 0) and a radius of 1, what is its equation?

Back

The equation is x² + y² = 1.

Front

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

Back

The general form is x² + y² + Dx + Ey + F = 0.