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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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