Question

Find the equations of the lines joining the vertex of the parabola y² = 6x to the point on it which have abscissa 24. 

Answer 1

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

\[y - 0 = \pm \frac{12 - 0}{24 - 0}(x - 0)\]
\[ \Rightarrow \pm 2y = x\]
\[\]