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Parabolas
Hyperbolas
Circles
Ellipses
Name That Conic
1

The graph of the function y = –2x^2 + 4x – 4 opens this direction.

What is downward?

1
These are the coordinates for the center of a hyperbola whose equation is [(x + 2)^2 / 3] – [(y – 3)^2 / 2] = 1.
What are (–2 , 3)?
1

What are the coordinates of the center of a circle whose equation is (y – 2)2 + (x + 3)2 = 4?

(–3 , 2)

1
These are the coordinates of the foci for an ellipse whose equation is x^2 / 25 + y^2 / 16 = 1.
What are (3 , 0) and (-3 , 0)?
1

6x2 + 12x – y + 15 = 0 is an equation for this type of conic section.

Parabola

2
This is the equation for the axis of symmetry of a parabola.
What is x = –b/2a?
2
A hyperbola whose equation is (y^2 / 4) – (x^2 / 9) = 1 opens in these directions.
What are up and down?
2

What is the radius of a circle whose equation is (x+5)2 + y^2 = 121.

11

2

These are the coordinates of the center of an ellipse whose equation is [x^2 / 4] + [(y – 2)^2 / 9] = 1

What are (0 , 2) ?

2

3x^2 + 3y^2 – 6x + 9y – 14 = 0 is an equation for this type of conic section.

Circle

3
This algebraic method will translate the equation of a parabola from standard form to vertex form.
What is Completing the Square?
3
These are the lines that are approached, but never touched, by the graph of a hyperbola.
What are asymptotes?
3

This is the radius of a circle whose equation is (2x^2 / 8) + (3y^2 / 12) = 1.

What is 2?

3
An ellipse whose equation is 9x^2 + 4y^2 = 36 has a major axis along this axis of the coordinate plane.
What is the y-axis?
3
x^2 + 2y^2 + 4x + 2y – 27 = 0 is an equation for this type of conic section.
What is an ellipse?
4
These are the roots, in simplest radical form, for the parabola whose equation is y = 3x^2 + 6x – 1.
What are (–3±2√3)/3?
4
A hyperbola whose equation is (x^2 / 16) – (y^2 / 9) = 1 has foci at these two coordinates.
What are (5 , 0) and (–5 , 0)?
4
This is the name of a segment containing the center of a circle whose endpoints are both on the circle.
What is a diameter?
4
This is the length of the minor axis for an ellipse whose equation is [(x – 1)^2 / 9] + [(y + 4)^2 / 16] = 1.
What is 6?
4
x2 – y2 + 3x – 2y – 43 = 0 is an equation for this type of conic section.
What is a hyperbola?
5

A baseball player throws a ball from the outfield toward home plate. The ball's height above the ground is modeled by the equation y = –16x^2 + 48x + 6, where y represents height, in feet, and x represents time, in seconds. The ball is initially thrown from a height of 6 feet. This is the maximum height that the ball reaches.

What is 42 feet?

5
This is the equation of a hyperbola whose vertices are at (0 , -3) and (0 , 3) and has a focus at (0 , 5).
What is (y^2 / 9) – (x^2 / 16) = 1?
5
A circle can be formed by slicing a right circular cone with a plane traveling THIS WAY in relation to the base of the cone.
What is parallel?
5
This is the equation of the ellipse whose foci are at (–1 , 0) and (3 , 0) and the length of its minor axis is 2.
What is [(x – 2)^2 / 5] + y^2 = 1
5
This type of conic section is a special case of an ellipse where a = b.
What is a circle?