AP EAMCET · Maths · Hyperbola
If the equation \(\frac{x^2}{7-k}+\frac{y^2}{5-k}=1\) represents a hyperbola then
- A \(5 \lt k \lt 7\)
- B \(k \lt 5\) or \(k\gt7\)
- C \(k\gt5\)
- D \(k \neq 5, k \neq 7,-\infty \lt k \lt \infty\)
Answer & Solution
Correct Answer
(A) \(5 \lt k \lt 7\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A} x^2+\mathrm{B} x y+\mathrm{C} y^2+\mathrm{D} x+\mathrm{E} y+\mathrm{F}=0\) represents a hyperbola if \(B^2-4 A C\gt0, A \neq C\) Given equation : \(\frac{x^2}{7-k}+\frac{y^2}{5-k}=1\) \(\Rightarrow \mathrm{A}=\frac{1}{5-k}, \mathrm{~B}=0, \mathrm{C}=\frac{1}{7-k}\)…
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