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AP EAMCET · Maths · Ellipse

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

  1. A \(|m|>1\)
  2. B \(|m| < 1\)
  3. C \(|m|>2\)
  4. D \(|m| < 2\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(|m| < 1\)

Step-by-step Solution

Detailed explanation

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,…