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Question
Find the equations of the lines joining the vertex of the parabola y2 = 6x to the point on it which have abscissa 24.
Solution
Let A and B be points on the parabola y2 = 6x and OA, OB be the lines joining the vertex O to the points A and B whose abscissa are 24.
Now,
y2 = 6 × 24 = 144
⇒ y = ± 12
Therefore the coordinates of the points A and B are (24, 12) and (24, –12) respectively.
Hence the lines are given by
\[ \Rightarrow \pm 2y = x\]
\[\]
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