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Find the maximum area of isoceles triangle inscribed in the ellipse x^2/a^2 + y^2/b^2 =1 with its vertex at one end of major axis ?( Please give a detailed explanation about how we use cosine and sines to form the equation as i am not getting that part . ) Thankyou

Find the maximum area of isoceles triangle inscribed in the ellipse x^2/a^2 + y^2/b^2 =1 with its vertex at one end of major axis ?( Please give a detailed explanation about how we use cosine and sines to form the equation as i am not getting that part . )
Thankyou

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
7 years ago
Take x and y in the polar form of the ellipse. Assume the vertiecs of the triangle on the elliipse. If I have the apex of the isoceles triangle in the x axis, the two equal sides of the triangle will extend to the either Ist and 4thOR 2ndand 3rd quadrant. Accordingly, name the coordinates polarity and find the area of the triangle using cartesian coordinates as you have coordinates of all the three vertices. Then substitute the x and y with their polar eqns as done in the first step. Then using the application of derivatives, find the maxima value using 2ndorder differentiation test.

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