WBJEE · Maths · Hyperbola
The line segment joining the foci of the hyperbola \(x^{2}-y^{2}+1=0\) is one of the diameters of a circle. The equation of the circle is
- A \(x^{2}+y^{2}=4\)
- B \(x^{2}+y^{2}=\sqrt{2}\)
- C \(x^{2}+y^{2}=2\)
- D \(x^{2}+y^{2}=2 \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(x^{2}+y^{2}=2\)
Step-by-step Solution
Detailed explanation
Given, equation of hyperbola is \[ x^{2}-y^{2}+1=0 \] \(\Rightarrow \quad y^{2}-x^{2}=1\) On comparing it with \(\frac{y^{2}}{b^{2}}-\frac{x^{2}}{a^{2}}=1,\) we get \[ a=b=1 \] Now, \(e=\sqrt{1+\frac{a^{2}}{b^{2}}}=\sqrt{1+\frac{1}{1}}=\sqrt{2}\) \(\therefore\) Foci…
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