Question

Determine the positions of the points (a) $(3,6),$ (b) $(4,3)$ and (c) $(1,-3)$ with respect to the parabola $y^2=9x$

Answer 1

Given Parabola:$y^2-9x$

$\left(a\right)$At $(3,6)$

$S=6^2-9\times 3=36-27=9>0$

Hence the point $(3,6)$ is outside the parabola.

$\left(b\right)$At $(4,3)$

$S=3^2-9\times 4=9-36=-27<0$

Hence the point $(4,3)$ is inside the parabola.

$\left(c\right)$At $(1,-3)$

$S={(-3)}^2-9\times 1=9-9=0$

Hence the point $(1,-3)$ is on the parabola.