Conic Sections Standard Form

A set of points  in a plane that are equidistant from a fixed line called directrix and fixed point called focus.

A set of all points such that the distance from a fixed point is constant.

It describes as the intersection of a plane and a double-napped cone.

It is generated when the plane is parallel to one generator and intersecting only one of its nappes.

CIRCLE

PARABOLA

ELLIPSE

HYPERBOLA

Horizontal

Vertical

If p > 0, parabola opens to the downward.

If p < 0 , parabola opens to the left.

If p < 0 , parabola opens to the right.

If p < 0 , parabola opens to the upward.

If a is located in the denominator of the x , the major axis is horizontal.       

If a is located in the denominator of the y , the major axis is horizontal.       

If b is located in the denominator of the x , the major axis is horizontal.

If b is located in the denominator of the y , the major axis is vertical.