WBJEE · Maths · Circle
The locus of the mid-points of chords of the circle \(x^{2}+y^{2}=1\), which subtends a right angle at the origin, is
- A \(x^{2}+y^{2}=\frac{1}{4}\)
- B \(x^{2}+y^{2}=\frac{1}{2}\)
- C \(x y=0\)
- D \(x^{2}-y^{2}=0\)
Answer & Solution
Correct Answer
(B) \(x^{2}+y^{2}=\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \((h, k)\) be the coordinates of the mid-point of a chord which subtends a right angle at the origin. Then, equation of the chord is \[ \begin{array}{l} \quad h x+h y-1=h^{2}+k^{2}-1 \quad[u \operatorname{sing} T=S] \\ \Rightarrow \quad h x+k y=h^{2}+k^{2} \end{array} \] The…
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