# Formulas for Parabola

**Formulas for Parabola**

Parabola is a Greek word which refers to a particular plane curve. In general words, parabola can also be define as a plane curve of the second degree. Parabola is a curve described by a projectile, moving on a non-resisting medium under the effect of gravity.

*The important formulas of parabola are listed below:-*

i. Different equations of parabola and some other relations are shown below:

Equaiton of parabola | Vertex | Focus | Equation of Directrix | Axis | Length of latus ration |

(0, 0) | (a, 0) | X = -a | Y = 0 | 4a | |

(0, 0) | (0, a) | Y = -a | X = 0 | 4a | |

(h, k) | (h +a, k) | X = h-a | Y = k parallel to x-axis | 4a | |

(h, k + a) | Y = k- a | X= h parallel to y-axis | 4a |

ii. The point lies on parallel if

The point lies out side if

The point lies in side if

iii. The line y = mx + c will intersect to parabola at two points if meet the parabola at coincident points if not cut the parabola if .

iv. The point lies on the parabola for any parameter t.

v. The equation of tangent to the parabola at is and tangent to the parabola at is .

vi. The condition of tangency of a straight line y = mx + c to a parabola is i.e. the line is always tangent to the parabola .

vii. Equation of normal at to the parabola is

**[ Note**: is equation of normal in m form.**]**

viii. are equation of pair of tangents to the parabola drawn from external point where

ix. represents the equation of chord of contact to the parabola drawn from and external point

x. represents the polar of the point with respect to the parabola

xi. is the pole of the line lx + my + x = 0 w.r.to the parabola

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