Question

The equations of the lines joining the vertex of the parabola y² = 6x to the points on it which have abscissa 24 are ______.

Options

• y ± 2x = 0

• 2y ± x = 0

• x ± 2y = 0

• 2x ± y = 0

Answer 1

The equations of the lines joining the vertex of the parabola y² = 6x to the points on it which have abscissa 24 are 2y ± x = 0.

Explanation:

Let P and Q be points on the parabola y² = 6x and OP

OQ be the lines joining the vertex O to the points P

And Q whose abscissa are 24.

Thus y² = 6 × 24 = 144

or y = ± 12.

Therefore the coordinates of the points P and Q are (24, 12) and (24, –12) respectively.

Hence the lines are y = `+-  12/24 x  2y  x`.