Conic Sections: Parabola, Ellipse And Hyperbola

THE PARABOLA

The parabola is a locus of points, equidistant from a given point, called the Focus and from a given line called the Directrix.

Equation of Tangent and Normal at point (x1,y1) to a Parabola

THE ELLIPSE

An ellipse is the locus of a point P, moving in a plane such that the sum of its distances from two fixed points F1 and F2 called the foci, is a constant.

THE HYPERBOLA

The hyperbola is the locus of a point P, moving in a plane such that the distance from two fixed points called the foci have a constant difference

The General Conic

A conicin general may be defined as the locus of a moving point P, such that its distance fixed Point called the focus, and its distance from a fixed line called the directrix are in constant ratio.

This constant ratio is called the eccentricity of the conic denoted by e. for

• a parabola              e = 1
  • an ellipse               e < 1
  • a hyperbola            e > 1

GENERAL EVALUATION

1. Write the equation of the ellipse, x² + 3y² + 2x –24y + 46 = 0 in the canonical form hence determine. Its vertices and foci
2. Find the vertices and foci of the hyperbola 25x² – 4y² = 100
3. Find the equation of the tangent and normal to the parabola y² – 18x = 0 at point (2,6)

READING ASSIGNMENT: New Further Mathematics Project 3 by TuttuhAdegun and Godspower5th Edition