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The tangent at any point on circle x^2+y^2=2 cuts the axes L and M then locus of midpoint of LM is:

The tangent at any point on circle x^2+y^2=2 cuts the axes L and M then locus of midpoint of LM is:
 

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
3 years ago
we see that radius of circle is root 2. now obviously any tangent to this circle will be at a distance of root 2 from the origin and vice-versa.
so, by the perpendicular form of a straight line, we can write the eqn of tangent as 
x cos α + y sin α = p= root2
now it cuts xaxis and y axis at root2secα and root2cosecα. so mid point would be (h,k) such that
2h=root2secα and 2k=root2cosecα
or 2cosα=root2/h and 2sinα=root2/k
squarng and adding
4=2(1/h^2+1/k^2)
or locus of mid point is 
1/x^2+1/y^2=2

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