If x cos α +y sin α = P is a tangent to the ellipse x²/a²+y²/b² = 1, then ?

Correct Answer is : a2²2cos2²2 α + b2²2 sin2²2α = P2²2

a²cos² α + b² sin²α = P²

a² sin² α + b² cos² α = P²

Correct Answer is : a2²2cos2²2 α + b2²2 sin2²2α = P2²2

Test Index

BITSAT 2019 Paper

Section: Mathematics

Question : 81 of 150

Marks: +1, -0

\frac{x^2}{a^2}+\frac{y^2}{b^2}

= 1, then ?

Solution:

Any tangent to the ellipse is

\frac{x\cos\theta}{a}+\frac{y\sin\theta}{b}

= 1 ....(2)

Comparing (1) and (2)

\frac{x\cos\theta}{a\cos\alpha}+\frac{y\sin\theta}{b\sin\alpha}=\frac{1}{P}

⇒ cosθ =

\frac{a\cos\alpha}{P}

and sinθ =

\frac{b\sin\alpha}{P}

Eliminate θ,

cos

^{2}

θ + sin

^{2}

θ=

\frac{a^2 \cos^2 a}{P^2}+\frac{b^2 \sin^2 a}{P^2}

a^2 \cos^2 \alpha

b^2 \sin^2 \alpha = P^2

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