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Question
Answer the following:
Find the Cartesian coordinates of the point on the parabola y2 = 12x whose parameter is 2
Solution
Given equation of the parabola is y2 = 12x.
Comparing this equation with y2 = 4ax, we get
4a = 12
∴ a = 3
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 = 3 and t = 2 in (i), we get
x = 3(2)2 and y = 2(3)(2)
∴ x = 12 and y = 12
∴ The cartesian co-ordinates of the point on the parabola are (12, 12).
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