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  • Find the coordinates of a point on the parabola y^2 = 8x whose focal distance is 4.

Find the coordinates of a point on the parabola y2 = 8x whose focal distance is 4.

Answers (1)

Given parabola is y2=8x

On comparing this parabola to the y2=4ax

we get a=2

Focal distance=Distance of any point on parabola from the focus SP=\sqrt{\left ( x_{1}-2 \right )^{2}+\left ( y_{1}-0\right )^{2}}

\sqrt{ x_{1}^{2}+ y_{1}^{2}-4x_{1}+4}+\sqrt{ x_{1}^{2}+ 8x_{1}-4x_{1}+4}=\left | x_{1}+2 \right |

|x1+2|=4

x1=2,-6 

 But x≠ -6 

 So for x=2

  y_{1}^{2}=8*2=16

  y= ±4  So the points are (2,4) and 2,-4 

Posted by

infoexpert22

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