AP EAMCET · Maths · Hyperbola
The difference between the focal distances of any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is 6 . If \((\sqrt{13}, k)\) is an end point of a latus rectum of this hyperbola, then \(\mathrm{k}=\)
- A \(\pm \frac{9}{2}\)
- B \(\pm \frac{8}{3}\)
- C \(\pm {9}\)
- D \(\pm \frac{4}{3}\)
Answer & Solution
Correct Answer
(D) \(\pm \frac{4}{3}\)
Step-by-step Solution
Detailed explanation
We have difference between foci \(=2 a\) \[ \therefore 2 a=6 \Rightarrow a=3 \text {, } \] \(\because\) End of focal chord is \(\left(c, \pm \frac{b^2}{a}\right) \Rightarrow c=\sqrt{13}\) \[ \because c^2=a^2+b^2 \Rightarrow 13=9+b^2 \Rightarrow b^2=4 \]…
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