if x=asin theta y=bcos theta eliminate theta
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x = a sinθ
Squaring on both sides , we get ,
⇒ x² = ( a sinθ )²
⇒ x² = a² sin²θ
⇒ x²/a² = sin²θ __ (1)
y = b cosθ
Squaring on both sides ,
⇒ y² = ( b cosθ )²
⇒ y² = b² cos²θ
⇒ y²/b² = cos²θ __ (2)
On adding (1) and (2) , we get ,
⇒ x²/a² + y²/b² = sin²θ + cos²θ
⇒ x²/a² + y²/b² = 1
[ From Trigonometric identity , sin²x + cos²x = 1 ]
Additionally , this equation x²/a² + y²/b² = 1 is called ellipse equation .
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