Q57 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

The line \(x=m^2\) meets an ellipse \(9 x^2+y^2=9\) in the real and distinct points if and only if

  • A
    \(|m|>1\)
  • Correct answer
    B
    \(|m| < 1\)
  • C
    \(|m|>2\)
  • D
    \(|m| < 2\)

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.

Hence, the correct answer is option: 'B'.

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