Question

The coordinates of the point on the parabola $y^2=18x$ whose ordinate is three times the abscissa, are $\underset{–}{}$

Answer 1

Equation of parabola is : $y^2=18x$

$\Rightarrow a=\frac{9}{2}$

Let a parametric point be $P(\frac{9}{2}{t}^2,9t)$

Given that-
$\text{ordinate of point P}=3\times \text{abscissa of point P}$

$\Rightarrow 9t=3\times \frac{9}{2}{t}^2$

$\Rightarrow t=\frac{3}{2}{t}^2$

$\Rightarrow t=\frac{2}{3}$

$\therefore \frac{9}{2}{t}^2=\frac{9}{2}\times {\left(\frac{2}{3}\right)}^2=2$

$9t=9\times \frac{2}{3}=6$

$\therefore P=(2,6)$

Hence, the coordinate of the point on the parabola $y^2=18x$ whose ordinate is three times the abscissa, are $(2,6)$.