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Question
Find the coordinates of points on the parabola y2 = 8x whose focal distance is 4.
Solution
We have y2 = 8x
⇒ y2 = 4(2)x
Comparing it with the general equation of parabola y2 = 4ax, we will get a = 2
Let the required point be (x1, y1)
Now, Focal distance = 4
⇒ x1 + a = 4
⇒ x1 + 2 = 4
⇒ x1 = 2
Now, the point will satisfy the equation of parabola
∴ (y1)2 = 8(2) = 16
⇒ y1 = ± 4
Hence, the coordiantes of the points are (2, 4) and (2, −4).
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