**Ap**

^{2}+ Bpq + Cq^{2}+ Dp + Eq + f = 0;If the value of B = 0 then we will see the ‘A’ and ‘C’ in the equations:

Name of conic section | Relationship of A and C |

Parabola | A = 0 or C = 0 but both the values of ‘A’ and ‘C’ are never equals to 0. |

Circle | In case of Circle the value of ‘A’ and ‘C’ are both equal. |

Ellipse | In case of ellipse the sign of ‘A’ and ‘C’ are same but ‘A’ and ‘C’ are not equal. |

Hyperbola | In case of hyperbola the signs of ‘A’ and ‘C’ are opposite. |

A line having curve shape is known as hyperbola. When the transverse axis of the given hyperbolas is aligned with the x – axis then the Equation of Hyperbola is given by:

⇒

$\frac{(p - h)^{2}}{a^{2}}$ - $\frac{(q-k)^{2}}{b^{2}}$ = 1

Having vertices - ( h $\pm$ a, k) and Foci (h $\pm$ c,k)

This is equation of hyperbola.

When the Intersection of Right Circular Cone and a plane which is also parallel to an element of the cone and the locus points of cone are equidistant from a fixed Point then we get a Plane Curve or a Parabola.

The general form is:

⇒ (αp + βq)

^{2}+ γp + δq + ∈= 0;

This above equation is obtained from the general conic sections equation which is given below:

⇒ Ap

^{2}+ Bpq + Cq

^{2}+ Dp + Eq + F = 0;

And the equations for a general form of parabola with the focus point F(s, t) and a directrix in the form:

⇒pa + qy + c = 0;

This is the equation of parabola.