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The Equation X 2 2 − λ + Y 2 λ − 5 + 1 = 0 Represents an Ellipse, If - Mathematics

MCQ
Sum

The equation \[\frac{x^2}{2 - \lambda} + \frac{y^2}{\lambda - 5} + 1 = 0\] represents an ellipse, if

Options

  •  λ < 5

  • λ < 2

  • 2 < λ < 5

  • λ < 2 or λ > 5

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Solution

\[2 < \lambda < 5\]

\[\frac{x^2}{2 - \lambda} + \frac{y^2}{\lambda - 5} + 1 = 0\]

\[ \Rightarrow \frac{x^2}{\lambda - 2} + \frac{y^2}{5 - \lambda} = 1\]

To represent the equation of ellipse, we have:

\[\lambda - 2 > 0\]

\[ \Rightarrow \lambda > 2\]

and

\[5 - \lambda > 0\]

\[ \Rightarrow 5 < \lambda\]

\[\therefore2 < \lambda < 5\]

Concept: Introduction of Ellipse
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Q 19 | Page 29
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