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Find the maximum length of chord of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` then find the locus of midpoint of PQ

Text Solution

Verified by Experts

The correct Answer is:
4
Let `P-=(2sqrt(3)cos theta, 2 sin theta)`
and `Q-=(2sqrt(3)cos((pi)/(2)+theta),2sin((pi)/(2)+theta))`
or `Q-=(-2sqrt(2)sin theta, 2 cos theta)`
`(PQ)^(2)=8(cos theta+sin theta)^(2)+4(sin theta-cos theta)^(2)=12+4 sin 2 theta`
`:. (PQ)_("max")=4`
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