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Grade 12th passIIT JEE Entrance Exam

Find the Locus of the mid points of the segments which are tangents to the ellipse
(x²/2)+(y²/1)=1
and which are intercepted between the coordinate axis

Profile image of manish nehra
7 Years agoGrade 12th pass
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1 Answer

Profile image of Anshuman Singh
7 Years ago
Any tangent to the given ellipse is xcos$/√2+ysin$=1 or x/(√2/cos$) + y/(1/sin$) =1
So mid point is 1/√2cos$,1/2sin$ now 
1/√2cos$=x and 1/2sin$=y  eliminating $we get 1/2x^2+1/4y^2 =1 which is the locus
 Eliminating $ by identity sin^2$ +cos^2$=1
 

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