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Question
Find coordinates of the point on the parabola. Also, find focal distance.
2y2 = 7x whose parameter is –2
Solution
Given equation of the parabola is 2y2 = 7x
∴ y2 = `7/2x`
Comparing this equation with y2 = 4ax, we get
4a = `7/2`
∴ a = `7/8`
If t is the parameter of the point P on the parabola, then
P(t) ≡ (at2, 2at)
i.e., x = at2 and y = 2at …(i)
Given, t = – 2
Substituting a = `7/8` and t = – 2 in (i), we get
x = `7/8(-2)^2` and y = `2(7/8)(-2)`
∴ x = `7/2` and y = `-7/2`
∴ The co-ordinates of the point on the parabola are `(7/2, -7/2)`.
Focal distance = x + a = `7/2 + 7/8 = 35/8`
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