If $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, b^{2} > a^{2},$ then prove that the equation of tangent at point (acos $θ$ , bsin $θ$ ) is $\frac{x}{a} c o s θ + \frac{y}{b} s i n θ = 1$

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Solution

Equation of tangent at $(x_{1}, y_{1})$ is $\frac{x x_{1}}{a^{2}} + \frac{y y_{1}}{b^{2}} = 1.$
Put $x_{1} = a c o s θ, y_{1} = b s i n θ$
$\frac{x}{a} c o s θ + \frac{y}{b} s i n θ = 1$

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