If tangents are drawn to the ellipse x²+2 y²=2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

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Correct answer: C. 1 2 x² + 1 4 y² =1

Given the equation of ellipse, x² ( 2 )² +y²=1 2 x 2 +y =1P ( 2 , 0 ) and Q (0, 1 ) Let mid point be (h, k) h= 1 2 , k= 1 2 As ² + ² =1 1 2 h² + 1 4 k² =1 Locus is 1 2 x² + 1 4 y² =1

If tangents are drawn to the ellipse x²+2 y²=2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

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