JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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
- A \(x^2 + y^2 -16x^2y^2 = 0\)
- B \(x^2 + y^2 -2x^2y^2 = 0\)
- C \(x^2 + y^2 -4x^2y^2 = 0\)
- D \(x^2 + y^2 -2xy = 0\)
Answer & Solution
Correct Answer
(C) \(x^2 + y^2 -4x^2y^2 = 0\)
Step-by-step Solution
Detailed explanation
Let the mid point be \(S(h,k)\) \(\therefore P\left( {2h,0} \right)\) and \(Q\left( {0,2k} \right)\) equation of \(PQ:\frac{x}{{2h}} + \frac{y}{{2k}} = 1\) \(\therefore PQ\) is tangent to circle at \(R\) (say)…
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