Question

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

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
$$\begin{gathered} y-0=\pm \frac{12-0}{24-0}(x-0) \\ \Rightarrow \pm 2y=x \end{gathered}$$