AP EAMCET · Maths · Hyperbola
If \(y=x+\sqrt{2}\) is a tangent to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{2}=1\), then equations of its directrices are
- A \(x= \pm \sqrt{3}\)
- B \(x= \pm \sqrt{\frac{8}{3}}\)
- C \(x= \pm \sqrt{\frac{2}{3}}\)
- D \(x= \pm \sqrt{\frac{4}{3}}\)
Answer & Solution
Correct Answer
(B) \(x= \pm \sqrt{\frac{8}{3}}\)
Step-by-step Solution
Detailed explanation
Hyperbola: \(\frac{x^2}{a^2}-\frac{y^2}{2}=1\). Now, equation of tangent in slope form \(y=m x \pm \sqrt{a^2 m^2-2}\) Comparing with given tangent line \(y=x+\sqrt{2}\) We get, \(m=1\) and \(a^2-2=2 \Rightarrow a^2=4\) \(e=\sqrt{1+\frac{2}{4}}=\sqrt{\frac{3}{2}} .\) So, equation…
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