ExamBro
ExamBro
COMEDK · Maths · 28. Indefinite Integration

The equation \(\dfrac{x^2}{2-\lambda}+\dfrac{y^2}{\lambda-5}+1=0\) represents an ellipse, if

  1. A \(\lambda <5\)
  2. B \(\lambda <2\) or \(\lambda>5\)
  3. C \(2 <\lambda <5\)
  4. D \(\lambda <2\)
Verified Solution

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…