The area of the parallelogram formed by the tangents at the points whose eccentr

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The area of the parallelogram formed by the tangents at the points whose eccentric angles are

θ, θ + \frac{π}{2}, θ + π, θ + \frac{3 π}{2}

on the ellipse

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

is

Options:

A . ab

B . 4ab

C . 3ab

D . 2ab

Answer: Option B
:
B

The Area Of The Parallelogram Formed By The Tangents At The ...

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

Area=

π a b

Let P

= (a c o s θ, b s i n θ)

S=(ae,0)
M(h,k) be the midpoint of PS

(h, k) = (\frac{a e + a c o s θ}{2}, \frac{b s i n θ}{2})

\frac{{(h - \frac{a e}{2})}^{2}}{{(\frac{a}{2})}^{2}} + \frac{k^{2}}{{(\frac{b}{2})}^{2}} = 1

A r e a = \frac{π a b}{4}

R a t i o = \frac{1}{4}

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