Equation of a Circle

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 can be found from its equation in standard form (x - h)² + (y - k)² = r², where the center is (h, k).

Front

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

Back

The radius of a circle represents the distance from the center of the circle to any point on the circle.

Front

If the equation of a circle is (x - 3)² + (y + 4)² = 121, what is the radius?

Back

The radius is 11, since the radius is the square root of 121.

Front

What is the center of the circle given by the equation (x - 7)² + y² = 9?

Back

The center of the circle is (7, 0).

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 the x and y terms.

Front

What is the equation of a circle with center at the origin and radius 5?

Back

The equation is x² + y² = 25.

Front

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

Back

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

Front

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

Back

Substitute the point's coordinates 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 relationship between the radius and diameter of a circle?

Back

The diameter of a circle is twice the radius (d = 2r).