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The equation $\large\frac{x^2}{5-a}+\frac{y^2}{4-a}$$=1$ represent ellipse if value of 'a' belongs to what value?

$\begin{array}{1 1}(a)\;a \in (-\infty,5)\\(b)\;a \in (-\infty,7)\\(c)\;a \in (-\infty,4)\\(d)\;\text{None of these}\end{array}$

1 Answer

it belongs to ellipse if
$5-a > 0$
$a < 5$
And also
$4-a > 0$
$a < 4$
Taking intersection we get,
$a \in (-\infty,4)$
Hence (c) is the correct answer.
answered Feb 7, 2014 by sreemathi.v

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