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  • P is a variable point on the ellipse   <img alt="\frac{\mathrm x^2}{\mathrm a^2}+\frac{\mathrm y^2}{\mathrm b^2}=1" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfrac%7B%5Cmathr

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

Option: 1

 ab
 


Option: 2

 2ab


Option: 3

 ab/2

 


Option: 4

none of these


Answers (1)

best_answer

Area of \Delta \mathrm {APA'}  will be maximum, when the height of triangle will be maximum i.e., \mathrm b
maximum area of    \Delta \mathrm{APA}=\frac{1}{2} \times 2 \mathrm{a} \times \mathrm{b}=\mathrm{ab}

Hence (1) is the correct answer.

Posted by

Divya Prakash Singh

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