InterviewSolution
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InterviewSolution
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Find the area of the region bounded by the latus recta of the ellipse `x^2/a^2+y^2/b^2=1` and the targets to the ellipse drawn at their ends |
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Answer» equation of tangent PR `(xx_1)/a^2+(yy_1)/b^2=1` putting the extreme values `(xe)/a+y/a`=1 -(1) equation of tangent QR `(xe)/a-y/b=1` -(2) adding 1 and 2 `(2xe)/a=2` `x=a/e` putting this value in equation 1 `(xe)/a+y/a=1` `a/e*e/a+y/a=1` y=0 we got point R(`a/e`,0) area of `triangle` PQR A=`1/2*PQ*FR` `A=1/2*(2b^2)/a*sqrt(a/e-ae)` `A=1/2*(2b^2)/a*sqrt(a(1/e-e)` `A=b^2/asqrt(a((1-e^2)/e)` `A=b^2/asqrt(b^2/(ae))` `A=b^2/asqrt(b^2/sqrt(a^2-b^2)` `a=b^3/(a(a^2-b^2)^(1/4)` |
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