Equations of Circles in Standard form

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 standard form (x - h)² + (y - k)² = r² is given by the point (h, k).

Front

What does the radius of a circle represent in its equation?

Back

The radius (r) in the equation (x - h)² + (y - k)² = r² represents the distance from the center of the circle to any point on the circle.

Front

If the equation of a circle is (x + 2)² + (y - 3)² = 25, what is the center and radius?

Back

The center is (-2, 3) and the radius is 5.

Front

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

Back

Substitute the point (x, y) into the circle's equation. If the result is less than r², the point is inside; if equal, on the circle; if greater, outside.

Front

What is the diameter of a circle?

Back

The diameter is twice the radius of the circle, represented as d = 2r.

Front

Write the equation of a circle with center (4, -1) and radius 2.

Back

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

Front

What is the relationship between the endpoints of a diameter and the center of a circle?

Back

The center of the circle is the midpoint of the diameter's endpoints.

Front

If a circle has a center at (0, 0) and a radius of 4, what is its equation?

Back

The equation is x² + y² = 16.

Front

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

Back

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