COMEDK · Maths · 28. Indefinite Integration
The equation \(\dfrac{x^2}{2-\lambda}+\dfrac{y^2}{\lambda-5}+1=0\) represents an ellipse, if
- A \(\lambda <5\)
- B \(\lambda <2\) or \(\lambda>5\)
- C \(2 <\lambda <5\)
- D \(\lambda <2\)
Answer & Solution
Correct Answer
(C) \(2 <\lambda <5\)
Step-by-step Solution
Detailed explanation
The given equation is \(\dfrac{x^2}{2-\lambda} + \dfrac{y^2}{\lambda-5} + 1 = 0\). Rearranging the equation, we get \(\dfrac{x^2}{\lambda-2} + \dfrac{y^2}{5-\lambda} = 1\). For this equation to represent an ellipse, the denominators must be positive and distinct. Thus, we…
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