Saturday, December 6, 2008

Equation of the chord joining any two points on an ellipse

If P(a cos θ, b sin θ) and Q( a cos ф,b sin ф) be any two points of the ellipse x²/a² + y²/b² = 1, then equation of chord joining P and Q is of the form

(y-y1) = m(x-x1) which is going to be

(y – b sin θ) = [(b sin ф - b sin θ)/( a cos ф - a cos θ)]*(x – a cos θ)

The equation can also be expressed as

(x/a)* cos [(θ+ ф)/2] +(y/b)*sin [(θ+ ф)/2] = cos [(θ- ф)/2]

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