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 given the endpoints of the diameter?

Back

The center of the circle is the midpoint of the diameter. If the endpoints are (x1, y1) and (x2, y2), the center is ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the radius of a circle?

Back

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

Front

If the diameter of a circle is 10, what is the radius?

Back

The radius is half of the diameter, so the radius is 5.

Front

What is the equation of a circle with center (0, 0) and radius 3?

Back

The equation is x² + y² = 9.

Front

How do you convert the equation (x - 2)² + (y + 3)² = 16 to standard form?

Back

The equation is already in standard form: (x - h)² + (y - k)² = r².

Front

What does the term 'h' represent in the circle equation (x - h)² + (y - k)² = r²?

Back

The term 'h' represents the x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the circle equation (x - h)² + (y - k)² = r²?

Back

The term 'k' represents the y-coordinate of the center of the circle.

Front

If a circle has a center at (2, -1) and a radius of 4, what is its equation?

Back

The equation is (x - 2)² + (y + 1)² = 16.

Front

What is the distance formula used to find the radius of a circle?

Back

The distance formula is d = √((x2 - x1)² + (y2 - y1)²).