Question

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

Answer 1

Equation of parabola , $y^2=9x$ or $y^2-9x=0$

a) at $(3,6)$

$6^2-9\left(3\right)=$$36-27=$$9$

So, It is positive which means $(3,6)$ is outside the parabola.

b) at $(4,3)$

$3^2-9\left(4\right)=$$9-36=-27$

So, It is negative which means $(4,3)$ is inside the parabola.

c) at $(1,-3)$

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

So, It is zero which means $(1,-3)$ is on the parabola.