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A point on the parabola y^{2}=18x at which the ordinate increases at twice the rate of the abscissa is

  • Option 1)

    \left ( \frac{-9}{8},\frac{9}{2} \right )\;

  • Option 2)

    \; (2,-4)\;

  • Option 3)

    \; (2,4)\;

  • Option 4)

    \; \left ( \frac{9}{8},\frac{9}{2} \right )\;

 

Answers (1)

As we learnt in

Standard equation of parabola -

y^{2}=4ax

- wherein

 

 y2=18x

Differentiating both sides, we get 

\frac{2ydy}{dt}=18\frac{dx}{dt}\\ Given \: \frac{dy}{dt}=2\frac{dx}{dt}\:at (x,y)

27\left(\frac{2dx}{dt} \right )=\frac{18dx}{dt}

y=\frac{9}{2}

Also\ y^{2}=18x\Rightarrow \left(\frac{9}{2} \right )^{2}=18x

So \:x=\frac{9}{8}

Point\ is \left (\frac{9}{8},\frac{9}{2} \right )


Option 1)

\left ( \frac{-9}{8},\frac{9}{2} \right )\;

This option is incorrect 

Option 2)

\; (2,-4)\;

This option is incorrect 

Option 3)

\; (2,4)\;

This option is incorrect 

Option 4)

\; \left ( \frac{9}{8},\frac{9}{2} \right )\;

This option is correct 

Posted by

Vakul

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