AP EAMCET · Maths · Hyperbola
If the equation of the hyperbola having \((8,3),(0,3)\) as foci and \(\frac{4}{3}\) as eccentricity is \(\frac{(x-\alpha)^2}{p}-\frac{(y-\beta)^2}{q}=1\) then \(p+q=\)
- A \(\beta^2\)
- B \(\alpha+\beta\)
- C \(\alpha^2\)
- D \(\alpha \beta\)
Answer & Solution
Correct Answer
(C) \(\alpha^2\)
Step-by-step Solution
Detailed explanation
\(\text{Center } (\alpha, \beta) = \left(\frac{8+0}{2}, \frac{3+3}{2}\right) = (4,3)\) \(\alpha=4, \beta=3\) \(2c = |8-0| = 8 \Rightarrow c=4\) \(e = \frac{c}{a} \Rightarrow \frac{4}{3} = \frac{4}{a} \Rightarrow a=3\)…
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