I received this email from my Engineering classmate,
Mahesh, I was looking at the old math notes from my engineering and came across this question. You had also solved it. I hope you remember answers for this in case your daughter who is attending Engineering asks.Find the positive value of such that the area enclosed by the ellipse x^2/9 + y^2=1, the x-axis, and the line y=2x/3 is equal to the area in the first quadrant enclosed by the ellipse x^2/9 + y^2=1, the y-axis, and the line y=mx.
I am assuming it is a valid question and my friend is not pulling my leg. When I say pulling my leg it is not related to my Math skills (which was very good in my student days) but he is testing my memory. I did not even attempt to solve the problem as I was blank as a clean slate.
In engineering days we had to “prove” few facts in Math. My friends who were very creative would scribble the workings and confidently end their answer with “Therefore LHS = RHS” (left-hand side = right-hand side). By any stretch of imagination, LHS was not resembling RHS. My friends knew it, my teachers knew about it. Anyway, all my friends are well settled now. Math had no bearing on their future.