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  • The equation <img alt="\mathrm{\frac{x^{2}}{16-a^{2}}-\frac{y^{2}}{9-a^{2}}=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7Bx%5E%7B2%7D%7D%7B16-a%5E%7B2%7D%7D-%5Cfrac

The equation \mathrm{\frac{x^{2}}{16-a^{2}}-\frac{y^{2}}{9-a^{2}}=1}represents an ellipse if and only if \mathrm{a \in}

Option: 1

(3,4)


Option: 2

(-4,-3)


Option: 3

(-4,-3) \cup(3,4)


Option: 4

none of these


Answers (1)

best_answer

 The given equation represents and ellipse if \mathrm{16-a^{2}>0, a^{2}-9>0\: and \: 16-\mathrm{a}^{2} \neq \mathrm{a}^{2}-9}
\mathrm{i.e., a \in(-4,4)\: and}
\mathrm{a \in(-\infty,-3) \cup(3, \infty)\: and \: a \neq \pm \frac{5}{\sqrt{2}}}
\mathrm{\Rightarrow \mathrm{a} \in(-4,-3) \cup(3,4)}
and \mathrm{a \neq \pm \frac{5}{\sqrt{2}}}.  Thus (D) is the correct answer.

Posted by

rishi.raj

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