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  • P is a variable point on the ellipse  <img alt="\mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfr

P is a variable point on the ellipse  \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}}  = 1 with AA′ as the major axis. Then the maximum value of the area of the triangle APA′ is

 

Option: 1

cbbv       ab

 

 

 


Option: 2

(B) b       2ab


Option: 3

ab /2


Option: 4

None of these


Answers (1)

best_answer

Area of  Δ APA′  will be   maximum  when  the   height  of  triangle will be  maximum as the  base  is  fixed.   Maximum height   will be equal to  b .

Maximum area of   \mathrm{\triangle \mathrm{APA}^{\prime}=\frac{1}{2} \times 2 \mathrm{a} \times \mathrm{b}=\mathrm{ab}} 

Hence (A) is the correct answer.

Posted by

himanshu.meshram

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