Question

For what point of the parabola $y^2=18x$ the ordinate equal to three times the abscissa ?

Answer 1

given parabola
$y^2=18x$
$y=3x$ given
putting value of y in above eqn we get
$(3x{)}^2=18x$
$9x^2=18x$
$x^2=2x$
$\therefore x=2,0$
for $x=0$ $\Rightarrow y=0$ point $(0,0)$
for $x=2$ $\Rightarrow y=6$ point $(2,6)$