The line \(x=m^2\) meets an ellipse \(9 x^2+y^2=9\) in the real and distinct points if and only if
The line \(x=m^2\) meets an ellipse \(9 x^2+y^2=9\) in the real and distinct points if and only if
\(|m|>1\)
\(|m| < 1\)
\(|m|>2\)
\(|m| < 2\)
Solution
Since, the line \(x=m^2\) meets the ellipse \(9 x^2+y^2=9\) in the real and distinct points, so on solving line and ellipse, we get
\(\begin{aligned}
& 9 m^4+y^2=9 & \Rightarrow y^2=9\left(1-m^4\right) > 0 \\
\Rightarrow & m^4 < 1 & \Rightarrow|m| < 1
\end{aligned}\)
Hence, option (b) is correct.