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Question
Find coordinates of the point on the parabola. Also, find focal distance.
y2 = 12x whose parameter is `1/3`
Solution
Given parabola is y2 = 12x
Comparing with y2 = 4ax, we get,
4a = 12
∴ a = 3
If a point P has parameter t, then P(t) = (at2, 2at)
Here, t = `1/3`
∴ P`(1/3) = (3 xx 1/9, 2 xx 3 xx 1/3)`
= `(1/3, 2)`
Focal distance of P
= a + x1, where x1 = `1/3`
= `3 + 1/3`
= `10/3`
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