EllipseMedium
Question
The equation to the locus of the middle point of the portion of the tangent to the ellipse 
= 1 included between the co-ordinate axes is the curve -
= 1 included between the co-ordinate axes is the curve -Options
A.9x2 + 16y2 = 4x2y2
B.16x2 + 9y2 = 4x2y2
C.3x2 + 4y2 = 4x2y2
D.9x2 + 16y2 = x2y2
Solution
Let any tangent of ellipse is
= 1
Let it meets axes at A
& B 
Let mid point of AB is (h, k) then
2h =
, 2k = 
Since cos2θ + sin2θ = 1
∴
= 1
⇒ 16k2 + 9h2 = 4h2k2
Hence locus is 16y2 + 9x2 = 4x2y2.
= 1Let it meets axes at A
& B Let mid point of AB is (h, k) then
2h =
, 2k = Since cos2θ + sin2θ = 1
∴
= 1⇒ 16k2 + 9h2 = 4h2k2
Hence locus is 16y2 + 9x2 = 4x2y2.
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