InterviewSolution
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InterviewSolution
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The muinimum area of the triangle formed by the tangent to `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` and the coordinate axes isA. ab sq. unitsB. `(a^(2)+b^(2))/(2)` sq. unitsC. `((a+b)^(2))/(2)` sq. unitsD. `(a^(2)+ab+b^(2))/(3)` sq. units |
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Answer» Tangent to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` at `p( a cos theta, b sin theta)` is given by `(xcos theta)/(a)+(y sin theta)/(b)=1` It meets he coordinate axes at `A(a sec theta, 0) and B(0, b "coses" beta)` or `Delta=(ab)/(sin 2 theta)` For area to be minimum, `sin theta` should be maxiumum and we know that teh maxiumum value of `sin theta` is 1. Therefore, `Delta_("max")=ab` |
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