COMEDK · Maths · 15. Hyperbola
If \(\frac{x^{2}}{36}-\frac{y^{2}}{k^{2}}=1\) is a hyperbola, then which of the following statements can be true?
- A \((3,1)\) lies on the hyperbola.
- B \((-3,1)\) lies on the hyperbola.
- C \((5,2)\) lies on the hyperbola.
- D \((10,4)\) lies on the hyperbola.
Answer & Solution
Correct Answer
(D) \((10,4)\) lies on the hyperbola.
Step-by-step Solution
Detailed explanation
We have, \[ \frac{x^{2}}{36}-\frac{y^{8}}{k^{2}}=1 \] Option (a) \((3,1)\) \[ \begin{aligned} \frac{9}{36}-\frac{1}{k^{2}} &=1 \\ \Rightarrow \quad & \frac{1}{k^{2}}=\frac{-27}{36} \Rightarrow k^{2}=\frac{-36}{27} \end{aligned} \] which is not possible. Option (b) \((-3,1)\)…
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