Equation frac{{{x^2}}}{{2 - r}} + frac{{{y^2}}}{{r - 5}} + 1 = 0 represents an ellipse, if

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10-2. Parabola, Ellipse, Hyperbola

easy

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

A

$r > 2$

B

$2 < r < 5$

C

$r > 5$

D

None of these

Solution

(b) $\frac{{{x^2}}}{{2 – r}} + \frac{{{y^2}}}{{r – 5}} + 1 = 0$

==>$\frac{{{x^2}}}{{r – 2}} + \frac{{{y^2}}}{{5 – r}} = 1$

Hence $r > 2$ and $r < 5$

==>$2 < r < 5.$

Standard 11

Mathematics

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