If a tangent to the circle x^2+y^2=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:

Question

Accepted Answer

Correct answer: A. (a) JEE Main 2019 Let any tangent to circle x^2+y^2=1 is x cos +y sin =1 Since, P and Q are the point of intersection on the co-ordinate axes. Then, P ≡ ( 1 cos ,0 )& Q= (0 , 1 sin ) ∴mid-point of PQ be M ≡ ( 12 cos , 12 sin ) ⇒ cos = 12h … (i) sin = 12k … (ii) Now squaring and adding equation (i) and (ii) 1h^2+ 1k^2=4 ⇒h^2+k^2=4h^2k^2 ∴locus of M is x^2+y^2=4x^2y^2

$If a tangent to the circle x^{2} + y^{2} = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:$

Solution

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