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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let the length of the latus rectum of an ellipse
$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $, $ (a > b) $, be $30$.
If its eccentricity is the maximum value of the function
$ f(t) = -\frac{3}{4} + 2t - t^2 $,
then $ (a^2 + b^2) $ is equal to
Solution
$ e^2 = \frac{1}{16} $
Then,
$ \frac{b^2}{a^2} = \frac{15}{16} $
$ b^2 = \frac{15}{16} a^2 $
$ \frac{2b^2}{a} = 30 $
$ \frac{2 \cdot 15}{16} a = 30 $
$ \frac{30}{16} a = 30 $
$ a = 16 $
$ b^2 = 240 $
$ a^2 = 256 $
$ a^2 + b^2 = 256 + 240 = 496 $
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