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

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

Back

In the equation of a circle, 'r' represents the radius of the circle.

Front

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

Back

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

Front

What is the radius of the circle given by the equation (x + 5)² + (y - 3)² = 36?

Back

The radius is 6, since r² = 36, thus r = √36 = 6.

Front

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

Back

The equation is x² + y² = 16.

Front

What is the center of the circle described by the equation (x - 1)² + (y + 2)² = 25?

Back

The center is (1, -2).

Front

If the radius of a circle is doubled, how does the area change?

Back

The area of a circle is given by A = πr². If the radius is doubled, the area increases by a factor of 4.

Front

What is the equation of a circle with center (-3, 4) and radius 5?

Back

The equation is (x + 3)² + (y - 4)² = 25.

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 distance between the center and a point on the circle?

Back

The distance from the center (h, k) to a point (x, y) on the circle is equal to the radius 'r'.