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X^2/A^2-Y^2/B^2=

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4X^2-9Y^2+32X-144Y-548

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•A plane crosses at a steep enough angle so that it crosses through both cones.
•A parabola will graph as 2 curves that mirror over the x or y axis.

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A hyperbola may be defined as the curve of intersection between a right circular conical surface and a plane that cuts through both halves of the cone. The other major types of conic sectionsare the ellipse and the parabola; in these cases, the plane cuts through only one half of the double cone.

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Y^2+6Y+12X-15

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Y^2=4AX

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•A parabola passes through the cone and is parallel to the side.
•Parabolas always equal 0 when plugged into the discriminant formula.

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A parabola is the set of all points equidistant from a line and a fixed point not on the line. The line is called the directrix, and the point is called the focus. The point on the parabola halfway between the focus and the directrix is the vertex.

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2X^2+Y^2-4X-4=0

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X^2/A^2+Y^2/B^2=

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•A plane passes through a cone at an angle but is not steep enough to be parallel to the side of the cone.
•An circle is an ellipse, but an ellipse is not a circle because an ellipse's radius is not the same at all points.

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In Euclidean geometry, the ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points (the foci) is constant.

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X^2+Y^2+2X+8Y+8=0

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•A circle occurs when a plane crosses through a cone at a 0° incline.
•A circle has the same radius at any point on the circle.

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X^2+Y^2=

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As a conic section, the circle is the intersection of a plane perpendicular to the cone's axis. The geometric definition of a circle is the locus of all points a constant distance r {\displaystyle r} from a point ( h , k ) {\displaystyle (h,k)} and forming the circumference (C).