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AP EAMCET202021 Sep 2020Evening ShiftMathematicsEllipseActual

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

Options

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

Correct answer

B. (|m| < 1 )

Step-by-step 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 ( aligned & 9 m^4+y^2=9 & y^2=9 (1-m^4 ) > 0 & m^4 < 1 & |m| < 1 aligned ) Hence, option (b) is correct.

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