Conic Sections Review

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.

Front

What is the standard form of a parabola that opens upwards?

Back

The standard form of a parabola that opens upwards is y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the standard form of a parabola that opens downwards?

Back

The standard form of a parabola that opens downwards is y = -a(x - h)² + k, where (h, k) is the vertex.

Front

What is the standard form of a parabola that opens to the right?

Back

The standard form of a parabola that opens to the right is x = a(y - k)² + h, where (h, k) is the vertex.

Front

What is the standard form of a parabola that opens to the left?

Back

The standard form of a parabola that opens to the left is x = -a(y - k)² + h, where (h, k) is the vertex.

Front

What are the characteristics of a hyperbola?

Back

A hyperbola consists of two separate curves called branches, and it has two foci, two vertices, and asymptotes that define its shape.

Front

What is the equation of a hyperbola centered at (h, k) with a horizontal transverse axis?

Back

The equation is (x - h)²/a² - (y - k)²/b² = 1.

Front

What is the equation of a hyperbola centered at (h, k) with a vertical transverse axis?

Back

The equation is (y - k)²/a² - (x - h)²/b² = 1.

Front

How do you find the vertices of a hyperbola?

Back

The vertices of a hyperbola are located a units away from the center along the transverse axis.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located inside the curve, where all points on the parabola are equidistant from the focus and the directrix.