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Direction Cosines of a Line Passing through Two Points

The focal dis...

Question

The focal distances of points on the parabola y² = 16x whose ordinate is twice the abscissa, is __________.

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Solution

Given parabola, y² = 16x − 4ax

y² = 16x
i.e. a = 4
Let us suppose co-ordinate of P are (t, 2t) [since ordinate is twice the abscissa.]
Since P lies an y²= 16x
i.e. (2t)² = 16(t)
i.e. 4t²= 16t
i.e. t(t − 4) = 0
i.e. t = 0 or t = 4
Since t = 0 is not possible
⇒ t = 4
Hence, co-ordinate of P are (4, 8)

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