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Find the coordinates of points on the pa...

Find the coordinates of points on the parabola `y^2=8x` whose focal distance is `4.`

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Given parabola is `y^(2) =8x`
On comparing this parabola to the `y^(2)`=4ax, we get…..(i)
`8x=4axrArra=2`
`therefore` Focal distance=`abs(x+a)=4`
`rArr abs(x+2)=4`
`rArr x+2=pm4`
`rArr x=2,-6`
But `xne-6`
For x=2, `y^(2)=8xx2`
`therefore y^(2)=16rArry=pm4`
So, the points are `(2,4)` and `(2,-4).`
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