Conic Sections Review

Front

What is the center of a hyperbola?

Back

The center of a hyperbola is the midpoint between its two foci and is represented as (h, k) in the standard form of the hyperbola's equation.

Front

What is the center of a shifted ellipse?

Back

The center of a shifted ellipse is the point (h, k) in the standard form of the ellipse's equation, where (h, k) represents the coordinates of the center.

Front

How do you find the center of a conic section given its equation?

Back

To find the center of a conic section, rewrite the equation in standard form and identify the values of (h, k).

Front

Convert the equation of a circle to standard form: x^2 + y^2 - 12x + 8y + 3 = 0.

Back

(x - 6)^2 + (y + 4)^2 = 49.

Front

What type of conic section is represented by the equation 3x^2 - y^2 - 11x + 4 = 0?

Back

Hyperbola.

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

Front

What is the standard form of a hyperbola's equation?

Back

The standard form of a hyperbola's equation is (x - h)^2/a^2 - (y - k)^2/b^2 = 1 or (y - k)^2/a^2 - (x - h)^2/b^2 = 1.

Front

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

Back

The standard form of an ellipse's equation is (x - h)^2/a^2 + (y - k)^2/b^2 = 1, where (h, k) is the center.

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the lengths of the semi-major and semi-minor axes are equal.

Front

What is the definition of a parabola?

Back

A parabola is a conic section that is formed by the intersection of a plane parallel to the axis of a cone.