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 center of a circle from its equation?

Back

The center of a circle in the equation (x-h)² + (y-k)² = r² is given by the point (h, k).

Front

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

Back

The radius is 4, since r² = 16, thus r = √16 = 4.

Front

What does the equation x² + y² = 25 represent?

Back

This represents a circle centered at (0, 0) with a radius of 5, since r² = 25.

Front

If the center of a circle is (2, -3) and the radius is 5, what is the equation of the circle?

Back

The equation is (x-2)² + (y+3)² = 25.

Front

What is the distance between the center (1, 1) and a point (4, 5) on the circle?

Back

The distance is 5, calculated using the distance formula: √((4-1)² + (5-1)²) = √(9 + 16) = √25 = 5.

Front

What is the significance of the value on the right side of the equation in a circle's equation?

Back

The value on the right side (r²) represents the square of the radius of the circle.

Front

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

Back

To convert, complete the square for both x and y terms in the general form Ax² + Ay² + Bx + Cy + D = 0.

Front

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

Back

The center is (-1, 2).

Front

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

Back

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