JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(H : \frac{ x ^{2}}{ a ^{2}}-\frac{y^{2}}{ b ^{2}}=1\), a \(>0, b >0\), be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is \(4(2 \sqrt{2}+\sqrt{14})\). If the eccentricity \(H\) is \(\frac{\sqrt{11}}{2}\), then value of \(a^{2}+b^{2}\) is equal to
- A \(89\)
- B \(90\)
- C \(87\)
- D \(88\)
Answer & Solution
Correct Answer
(D) \(88\)
Step-by-step Solution
Detailed explanation
\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) Given \(e^{2}=1+\frac{b^{2}}{a^{2}} \Rightarrow \frac{11}{4}=1+\frac{b^{2}}{a^{2}} \Rightarrow b^{2}=\frac{7}{4} a^{2}\) \(\therefore \frac{x^{2}}{(a)^{2}}-\frac{y^{2}}{\left(\frac{\sqrt{7}}{2} a\right)^{2}}=1\) Now given…
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