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 is (x-h)² = 4p(y-k), where (h,k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the equation of a hyperbola with a horizontal transverse axis?

Back

The standard form is (x-h)²/a² - (y-k)²/b² = 1, where (h,k) is the center, a is the distance to the vertices, and b is the distance to the co-vertices.

Front

How do you determine the direction a parabola opens based on its equation?

Back

If the coefficient of (y-k) is positive, the parabola opens upwards; if negative, it opens downwards. For (x-h)², positive means it opens right, negative means left.

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, and the sum of the distances from any point on the ellipse to the foci is constant.

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where both foci coincide at the center, and the distances from the center to the edge are equal in all directions.

Front

What is the standard form of an ellipse with a vertical major axis?

Back

The standard form is (x-h)²/b² + (y-k)²/a² = 1, where a > b, (h,k) is the center, and a is the distance to the vertices along the y-axis.

Front

What is the relationship between the vertices and foci of a hyperbola?

Back

For a hyperbola, the distance from the center to each vertex is 'a', and the distance from the center to each focus is 'c', where c² = a² + b².

Front

What is the equation of a parabola that opens to the left?

Back

The standard form is y² = -4px, where (0,0) is the vertex and p is the distance from the vertex to the focus.

Front

How do you find the directrix of a parabola?

Back

The directrix of a parabola is a line that is perpendicular to the axis of symmetry and is located at a distance 'p' from the vertex in the opposite direction of the focus.