if tangents are drawn to the ellipse x2 + 2y2=2 at all points on the ellipse other than it's four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve
Answer (1)
Student Expert
9th Nov, 2019
Dear Shruti, I guess you want to know the locus of mid-point of intercept made by tangents between the axes.
We know that the equation of line with (h,k) as mid-point of intercept between the coordinate axis is x/2h + y/2k = 1. …... (1)
Equation of tangent to ellipse x2+2y2 = 2 is y = mx±√2m2+1 ….. (2)
Comparing both these equations, we have (2k)2 = 2.k2/h2 + 1
Hence, 1/4y2 + 1/2x2 = 1 is the required answer.
All the best
Hope this helps
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