Equation of a Circle

Front

What is the standard equation of a circle?

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What do the variables h and k represent in the equation of a circle?

Back

h and k represent the x and y coordinates of the center of the circle.

Front

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

Back

r represents the radius of the circle.

Front

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

Back

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

Front

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

Back

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

Front

Convert the equation x² + y² = 25 into standard form. What is the center and radius?

Back

Standard form: (x - 0)² + (y - 0)² = 25; Center: (0, 0), Radius: 5.

Front

What is the center of the circle in the equation (x + 2)² + (y - 4)² = 9?

Back

The center is (-2, 4).

Front

If a circle has a center at (3, -1) and a radius of 2, what is its equation?

Back

The equation is (x - 3)² + (y + 1)² = 4.

Front

What is the distance between the center (1, 2) and a point (4, 6) on the circle?

Back

The distance is 5 units, calculated using the distance formula.

Front

How do you determine if a point lies inside, on, or outside a circle?

Back

Calculate the distance from the center to the point and compare it to the radius.