Area of a triangle formed by tangent and normal to the curve x^2a^2+ y^2b^2=1 at p ( a 2 , b 2 ) with the X-axis is

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Correct answer: D. (d) : Equation of tangent at P ( a 2 , b 2 ) is, x (a/ 2 )a^2+y (b/ 2 )b^2=1. ( ∵ ) Tangent at (x_1 ,y_1 ) is ( xx_1a^2+ yy_1b^2=1) ⇒ xa+ yb= 2 (i) Equation of normal at P ( a 2 , b 2 ) is, a^2x (a/ 2 )- b^2y (b/ 2 )=a^2-b^2 ⇒ ax- by= a^2-b^2 2 (ii) Putting y=0 in (i), x=a 2 Also putting y=0 in (ii), x= a^2-b^2a 2 So, area of = 12 ((( a^2-b^2a 2-a 2) b 2) ) = 12 ((-a^2-b^2) b2a)= b(a^2+b^2)4a

$Area of a triangle formed by tangent and normal to the curve \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 at p (\frac{a}{2}, \frac{b}{2}) with the X -axis is$

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