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  • The line meets the ellipse <img alt="\mathrm{{x^{2}+\frac{y^{2}}{9}}=1}" src="htt

The line \mathrm{x=t^{2}} meets the ellipse \mathrm{{x^{2}+\frac{y^{2}}{9}}=1} in the real and distinct points if and only if

Option: 1

\mathrm{|t|<2}


Option: 2

\mathrm{|t|<1}


Option: 3

\mathrm{|t|>1}


Option: 4

none of these


Answers (1)

best_answer

 Solving the given line and the ellipse, we get \mathrm{t}^{2}+\frac{\mathrm{y}^{2}}{9}=1 \Rightarrow \mathrm{y}^{2}=9\left(1-\mathrm{t}^{2}\right), which gives real and distinct values of \mathrm{y}, if \mathrm{1-\mathrm{t}^{2}>0 \Rightarrow \mathrm{t} \in(-1,1)}.

Hence (B) is the correct answer.

Posted by

Gunjita

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