Table of Contents

Toggle**Introduction**

A conic is the locus of a point whose distance from a fixed point bears a constant ratio to its distance from a fixed line. The fixed point is the focus S and the fixed line is the directrix l

The constant ratio is called the eccentricity denoted by ‘e’

- if 0 < e < 1, the conic is an ellipse.
- e = 1, conic is a parabola
- e > 1, conic is a hyperbola.

**Important Terms Related to Parabola**

**Axis:**A line perpendicular to thee directrix and passes through the focus.**Vertex:**The intersection point of the conic and axis.**Centre:**The point which bisects every chord of the conic passing through it.**Focal Chord:**Any chord passing through the focus.**Latus Rectum:**A double ordinate passing through the focus of the parabola.

## Standard Form of a Parabola and Related Terms

Equation of Parabola |
(y – β)^{2} = 4a (x – α) |

Vertex |
(α, β) |

Focus |
(a + α, β) |

Equation of axis |
Parallel to x – axis |

Equation of directrix |
x + a = α |

Eccentricity |
1 |

Extremities of Latus Rectum |
(α + a, β + 2a) and (α + a, β – 2a) |

Length of Latus Rectum |
4a |

Equation of Parabola |
(x – α)^{2} = 4a (y – β) |

Vertex |
(α, β) |

Focus |
(α, a + β) |

Equation of axis |
Parallel to y – axis |

Equation of directrix |
y + a = β |

Eccentricity |
1 |

Extremities of Latus Rectum |
(α + 2a, β + a) and (α – 2a, β + a) |

Length of Latus Rectum |
4a |

## Position of a Point

The point (x1, y1) lies outside, on or inside the parabola y^{2} = 4ax according as y_{1} – 4ax_{1} >, =, < 0.

y_{1} – 4ax_{1} > 0 |
outside the parabola |

y_{1} – 4ax_{1} = 0 |
on the parabola |

y_{1} – 4ax_{1} < 0 |
inside the parabola |