Circles & Ellipses

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

What does the radius of a circle represent?

Back

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

Front

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

Back

To find the center of a circle from its equation in standard form (x-h)² + (y-k)² = r², the center is (h, k).

Front

What is the relationship between the diameter and radius of a circle?

Back

The diameter of a circle is twice the length of the radius. Diameter = 2 * Radius.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

What is the general form of the equation of a circle?

Back

The general form of the equation of a circle is x² + y² + Dx + Ey + F = 0.

Front

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

Back

To convert, complete the square for the x and y terms.

Front

What is the significance of the term 'F' in the general form of a circle's equation?

Back

The term 'F' affects the position of the circle but does not directly influence its size.

Front

What is an ellipse?

Back

An ellipse is a shape formed by the set of points where the sum of the distances from two fixed points (foci) is constant.

Front

What is the standard form of the equation of an ellipse?

Back

The standard form is (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.