Equations of Circles

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 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 a circle in the equation (x-h)² + (y-k)² = r²?

Back

The center of the circle is the point (h, k).

Front

If the equation of a circle is x² + y² = 25, what is the radius?

Back

The radius is 5, since r² = 25.

Front

What does the term 'h' represent in the circle equation (x-h)² + (y-k)² = r²?

Back

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

Front

What does the term 'k' represent in the circle equation (x-h)² + (y-k)² = r²?

Back

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

Front

How do you convert the general form of a circle's equation to standard form?

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

What is the radius of the circle with equation (x-3)² + (y+4)² = 36?

Back

The radius is 6, since r² = 36.

Front

What is the center of the circle with equation (x+2)² + (y-5)² = 49?

Back

The center is (-2, 5).

Front

If a circle has a radius of 10, what is the equation of the circle centered at (0, 0)?

Back

The equation is x² + y² = 100.