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Find the equation of the tangent and the normal to the given curve at the indicated point: x2/a2 + y2/b2 = 1 at (a cos θ, b sin θ)

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Consider y = x2/a2 + y2/b2 = 1 as the equation of curve

By differentiating both sides w.r.t. x

Here the equation of the normal at point (a cos θ, b sin θ)

On further calculation

yb cos θ – b2 sin θ cos θ = ax sin θ – a2 sin θ cos θ

It can be written as

a2 sin θ cos θ – b2 sin θ cos θ = ax sin θ – by cos θ

By taking sin θ cos θ as common

sin θ cos θ(a2 – b2) = ax sin θ – by cos θ

It can be written as

ax sec θ – by cosec θ = a2 – b2

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