Q. 143.7( 3 Votes )

Find the co

Answer :

Given that we need to find the coordinates of points on the parabola y2 = 8x whose focal distance is 4.



We know that the focal distance is the distance from the focus to any point on the parabola.


Comparing the given parabola with standard parabola y2 = 4ax. We get,


4a = 8


a = 2


focus = (a, 0) = (2, 0)


We know that point on y2 = 4ax is represented by (at2, 2at), where t is any real number.


The point on y2 = 8x is (2t2, 4t)


We know that the distance between two points (x1, y1) and (x2, y2) is .



16 = 4 + 4t4 - 8t2 + 16t2


16 = 4t4 + 8t2 + 4


4 = t4 + 2t2 + 1


4 = (t2 + 1)2


t2 + 1 = 2


t2 = 1


t = ±1


The points on parabola is,


(2t2, 4t) = (2(±1)2, 4(±1))


(2t2, 4t) = (2, ±4)


The points on parabola is (2, ±4).


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