JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
A circle touches both the \(y\)-axis and the line \(x+y=0\). Then the locus of its center is
- A \(y=\sqrt{2} x\)
- B \(x=\sqrt{2} y\)
- C \(y ^{2}- x ^{2}=2 xy\)
- D \(x^{2}-y^{2}=2 x y\)
Answer & Solution
Correct Answer
(D) \(x^{2}-y^{2}=2 x y\)
Step-by-step Solution
Detailed explanation
Let \((h, k)\) is centre of circle \(\left|\frac{ h - k }{\sqrt{2}}\right|=| h |\) \(k ^{2}- h ^{2}+2 h k =0\) \(\therefore\) Equation of locus is \(y ^{2}- x ^{2}+2 xy =0\)
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