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Question
For the parabola y2 = 4x, find the coordinate of the point whose focal distance is 17
Solution
Given parabola is y2 = 4x
Comparing with y2 = 4ax, we get,
4a = 4
∴ a = 1
Let P(x1, y1) be he required point on the parabola y2 = 4x, whose focal distance is 17.
∴ x1 + a = 17, where a = 1
∴ x1 + 1 = 17
x1 = 16
Since P(x1, y1) lies on y2 = 4x,
`y_1^2` = 4x1
∴ `y_1^2` = 4(16) = 64
∴ y1 = ± 8
Hence, coordinates of required points on the parabola are (16, 8) and (16, – 8).
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