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Major Axis of Ellipse

If x=acosθ ...

Question

If $x = a cos θ$ and $y = b sin θ$ then $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} =$

A

a^{2}

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B

b^{2}

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C

1

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D

a^{2} + b^{2}

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Solution

The correct option is A 1
$\frac{x}{a} = cos θ a n d \frac{y}{a} = sin θ$
Square and add to get 1

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Similar questions

x = a cos θ + b sin θ

y = a sin θ - b cos θ

a^{2} + b^{2} = x^{2} + y^{2}

.

x = a sin θ + b cos θ

y = a cos θ - b sin θ

, then prove that

x^{2} + y^{2} = a^{2} + b^{2}

\frac{x}{a} cos θ + \frac{y}{b} sin θ = 1 a n d \frac{x}{a} sin θ - \frac{y}{b} cos θ = 1

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

Q. If x = a cos θ and y = b sin θ, then b²x² + a²y² =

(a) a² b²
(b) ab
(c) a⁴ b⁴
(d) a² + b²

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, b^{2} > a^{2},

then prove that the equation of tangent at point (acos

θ

θ

\frac{x}{a} c o s θ + \frac{y}{b} s i n θ = 1

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