AP EAMCET · Maths · Ellipse
The equation \(\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0\) represents an ellipse if
- A \(r>2\)
- B \(r>5\)
- C \(2 < r < 5\)
- D \(r < 2 \text { or } r>5\)
Answer & Solution
Correct Answer
(C) \(2 < r < 5\)
Step-by-step Solution
Detailed explanation
The equation is \\(\\frac{x^2}{r-2}+\\frac{y^2}{5-r}=1\\). For an ellipse, the denominators must be positive: \(r-2 > 0 \Rightarrow r > 2\) \(5-r > 0 \Rightarrow r \(2 < r < 5\)
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