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The normal at the point (bt_{1}\: ^{2},2bt_{1}) on a parabola meets the parabola again in the point (bt_{2}\: ^{2},2bt_{2}), then

  • Option 1)

    t_{2}=-t_{1}+\frac{2}{t_{1}}\;

  • Option 2)

    \; t_{2}=t_{1}-\frac{2}{t_{1}}\;

  • Option 3)

    \; t_{2}=t_{1}+\frac{2}{t_{1}}\;

  • Option 4)

    \; t_{2}=-t_{1}-\frac{2}{t_{1}}

 

Answers (1)

best_answer

As we learnt in 

Parametric coordinates of parabola -

x= at^{2}

y= 2at

- wherein

For the parabola.

y^{2}=4ax

 If t_{1} \ and \ t_{2} are the parameters

t_{2} = -t_{1}-\frac{2}{t_{1}}

 


Option 1)

t_{2}=-t_{1}+\frac{2}{t_{1}}\;

This option is incorrect.

Option 2)

\; t_{2}=t_{1}-\frac{2}{t_{1}}\;

This option is incorrect.

Option 3)

\; t_{2}=t_{1}+\frac{2}{t_{1}}\;

This option is incorrect.

Option 4)

\; t_{2}=-t_{1}-\frac{2}{t_{1}}

This option is correct.

Posted by

prateek

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