AP EAMCET · Maths · Hyperbola
Let the transverse axis of a hyperbola \(\mathrm{H}\) be parallel to the \(X-\) axis and \(x^2+y^2-2 x-4 y+3=0\) be the equation of the auxiliary circle of \(\mathrm{H}\). If the asymptotes of \(\mathrm{H}\) are at right angles, then the equation of the hyperbola is
- A \(3 x^2-2 y^2-6 x+8 y-11=0\)
- B \(x^2-y^2+2 x+4 y-5=0\)
- C \(3 x^2-2 y^2+6 x+8 y-11=0\)
- D \(x^2-y^2-2 x+4 y-5=0\)
Answer & Solution
Correct Answer
(D) \(x^2-y^2-2 x+4 y-5=0\)
Step-by-step Solution
Detailed explanation
Centre of auxiliary circle \(=\) centre of hyperbola \(=(1,2)\) length of transverse axis = Diameter of auxiliary circle \(=2 \mathrm{a}=2 \sqrt{1+4-3} \Rightarrow \mathrm{a}=\sqrt{2}\) A hyperbola whose asymptotes are at right angles to each other is rectangular hyperbola i.e.…
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