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Question
Find the focal distance of a point on the parabola y2 = 16x whose ordinate is 2 times the abscissa
Solution
Given equation of the parabola is y2 = 16x
Comparing this equation with y2 = 4ax, we get
4a = 16
∴ a = `16/4` = 4
Since ordinate is 2 times the abscissa,
y = 2x
Substituting y = 2x in y2 = 16x, we get
(2x)2 = 16x
∴ 4x2 = 16x
∴ 4x2 – 16x = 0
∴ 4x(x – 4) = 0
∴ x = 0 or x = 4,
When x = 4,
focal distance = x + a = 4 + 4 = 8
When x = 0,
focal distance = a = 4
∴ Focal distance is 4 or 8.
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