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Let L1 be the length of the common chord of the curves x2 + y2 = 9 and y2 = 8x, and  L2 be the length of the latus rectum of     y2 = 8x, then :

  • Option 1)

    L_{1 }> L_{2}\;

  • Option 2)

    L_{1 }= L_{2}\;

  • Option 3)

    L_{1 }< L_{2}\;

  • Option 4)

    \frac{L_{1 }}{L_{2}} = \sqrt{2}

 

Answers (1)

best_answer

As we learnt in

Length of the latus rectum -

4a

 

- wherein

For the parabola.

y^{2}=4ax

 

 For points of intersection of x^{2}+y^{2}=3 and y^{2}=8x

x^{2}+8x-9=0

x=-9, 1

For \: \: x=1 \: \: \: \: ; \: \: y=\pm 2\sqrt{2}

So length of AB=4\sqrt{2}

legnth of Latus Rectum= 4a = 4\times 2 = 8.

Clearly, L_{1}< L_{2}

 

 


Option 1)

L_{1 }> L_{2}\;

This option is incorrect.

Option 2)

L_{1 }= L_{2}\;

This option is incorrect.

Option 3)

L_{1 }< L_{2}\;

This option is correct.

Option 4)

\frac{L_{1 }}{L_{2}} = \sqrt{2}

This option is incorrect.

Posted by

prateek

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