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  2. Please,please help me - If the vertices of a hyperbola be atandand one of its foci be at, then which one of the followi - Co-ordinate geometry - JEE Main
# Engineering

If the vertices of a hyperbola be at \left ( -2,0 \right ) and \left ( 2,0 \right ) and one of its foci be at \left ( -3,0 \right ), then which one of the following points does not lie on this hyperbola ? 

  • Option 1)

    \left ( 4,\sqrt{15} \right )

     

     

     

  • Option 2)

    \left ( 2\sqrt{6},5 \right )

  • Option 3)

    \left ( 6,5\sqrt{2} \right )

  • Option 4)

    \left ( -6,2\sqrt{10} \right )

Answers (1)
A admin

 

Standard equation of parabola -

y^{2}=4ax

- wherein

 

Given, equation of hyperbola  \frac{x^{2}}{4}-\frac{y^{2}}{b^{2}}=1

Given

ae=-3

=>b^{2}=a^{2}e^{2}-a^{2}

put a = 2 

=>b^{2}=5

Hence , equation of hyperbola is 

 \frac{x^{2}}{4}-\frac{y^{2}}{5}=1

Hence (6,5\sqrt2) does not lie on hyperbola.


Option 1)

\left ( 4,\sqrt{15} \right )

 

 

 

Option 2)

\left ( 2\sqrt{6},5 \right )

Option 3)

\left ( 6,5\sqrt{2} \right )

Option 4)

\left ( -6,2\sqrt{10} \right )

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