AP EAMCET · Maths · Hyperbola
If \(c\) is a real number and \(\frac{x^2}{c-12}+\frac{y^2}{7-c}=1\) represents a hyperbola, then
- A \(7 < c < 12\)
- B \(c < 7\)
- C \(c>12\)
- D \(c < 7 \text { or } c>12\)
Answer & Solution
Correct Answer
(D) \(c < 7 \text { or } c>12\)
Step-by-step Solution
Detailed explanation
For a hyperbola, denominators must have opposite signs. \((c-12)(7-c) \(-(c-12)(c-7) \((c-12)(c-7) > 0\) \(c 12\)
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