Conic Section: Review

Front

What is a conic section?

Back

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

Front

What is the standard form of a hyperbola?

Back

The standard form of a hyperbola is (x-h)²/a² - (y-k)²/b² = 1 or (y-k)²/a² - (x-h)²/b² = 1, where (h,k) is the center.

Front

What does the term 'vertex' refer to in conic sections?

Back

The vertex is a point where the curve changes direction. For parabolas, it is the highest or lowest point.

Front

How do you determine the direction a parabola opens?

Back

A parabola opens upwards if the coefficient of the squared term is positive and downwards if it is negative.

Front

What is the general equation of a circle?

Back

The general 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 is the difference between an ellipse and a hyperbola?

Back

An ellipse is a closed curve with two foci, while a hyperbola consists of two separate curves (branches) with two foci.

Front

What is the focus of a conic section?

Back

The focus is a fixed point used to define and construct conic sections. It is located at a specific distance from the vertex.

Front

What is the directrix in relation to a parabola?

Back

The directrix is a line used in the definition of a parabola. A point on the parabola is equidistant from the focus and the directrix.

Front

How can you identify a hyperbola from its equation?

Back

A hyperbola can be identified by the presence of a subtraction between squared terms in its standard form equation.

Front

What is the equation of a parabola that opens upwards?

Back

The equation of a parabola that opens upwards is in the form y = a(x-h)² + k, where a > 0.