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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

If m is a variable, the locus of the point of intersection of the...

If m is a variable, the locus of the point of intersection of the lines& x3−y2=m\dfrac{\text{x}}{3} - \dfrac{\text{y}}{2} = \text{m} and x3+y2=1m\dfrac{\text{x}}{3} + \dfrac{\text{y}}{2} = \dfrac{1}{\text{m}} is a/an :

Options

  1. AParabola
  2. BEllipse
  3. CHyperbola
  4. DNone of these

Correct answer

C. Hyperbola

Step-by-step solution

The required locus is obtained by eliminating the variable m from the given equations of the lines, then we have

\left(\dfrac{\text{x}}{3} - \dfrac{\text{y}}{2}\right) \left(\dfrac{\text{x}}{3} + \dfrac{\text{y}}{2}\right) = \text{m} \left(\dfrac{1}{\text{m}}\right)

→ \dfrac{x^{2}}{9} - \dfrac{y^{2}}{4} =11

This is clearly a hyperbola.
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