Question

The equations of the lines joining the vertex of the parabola y² = 6x to the points on it which have abscissa 24 are
(a) y ± 2x = 0
(b) 2y ± x = 0
(c) x ± 2y = 0
(d) 2x ± y = 0

Answer 1

Given parabola is y² = 6x
Equation of line joining the vertex of parabola to the point on it which have abscissa 24
$\begin{array}{rcl}\mathrm{i}.\mathrm{e}.\mathrm{for}{y}^2& =& 6\times 24\\ y& =& \pm 6\times 2=\pm 12\\ & & \mathrm{point}\mathrm{is}\left(24,\pm 12\right)\end{array}$
Hence, equation of live through (0, 0) and (24, $\pm$12) is y = mx
$$\begin{gathered} \mathrm{i}.\mathrm{e}.y=\frac{\pm 12}{24}x \\ \mathrm{i}.\mathrm{e}.2y\pm x=0 \end{gathered}$$
Hence, the correct answer is option B.