Circles and Ellipses Review

Front

What are the vertices of the ellipse?

Back

The vertices of the ellipse are the points where the ellipse intersects its major axis. For example, in the ellipse with vertices (3, -5) and (3, 7), these points are the farthest points along the vertical direction.

Front

What is the equation of a circle?

Back

The standard equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. For example, (x - 3)² + (y + 4)² = 9 represents a circle centered at (3, -4) with a radius of 3.

Front

What does (h,k) stand for in the standard circle equation?

Back

In the standard circle equation, (h,k) represents the center of the circle.

Front

What is the center of the circle given by the equation (x + 4)² + (y + 3)² = 16?

Back

The center of the circle is (h, k) = (-4, -3).

Front

What is the value of b in the ellipse equation x²/a² + y²/b² = 1?

Back

In the ellipse equation, b represents the semi-minor axis length. For example, if b = 3, the semi-minor axis is 3 units long.

Front

What is the relationship between the major and minor axes of an ellipse?

Back

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter. The lengths of these axes determine the shape of the ellipse.

Front

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

Back

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

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula A = πr², where r is the radius.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is given by the formula C = 2πr, where r is the radius.

Front

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

Back

The standard form of the equation of an ellipse 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.