Question

Write down the parametric coordinates of any point on each of the following parabolas.
(a) y^2=8x
b) y^2 =24x
c) y^2 =-16x
d)x^2 =6y

Answer 1

(a) The parametric coordinates of any point on parabola $y^2 = 8x$ :

\begin{cases} x = \dfrac {t^2} 8 \\ y = t \end{cases} \

$-\infin < t < \infin$

(b) The parametric coordinates of any point on parabola $y^2 = 24x$:

\begin{cases} x = \dfrac {t^2} {24} \\ y = t \end{cases} \

$-\infin < t < \infin$

(c) The parametric coordinates of any point on parabola $y^2 = - 16 x$ :

\begin{cases} x = -\dfrac {t^2} {16} \\ y = t \end{cases} \

$-\infin < t < \infin$

(d) The parametric coordinates of any point on parabola $x^2 = 6y$ :

\begin{cases} x = t \\ y = \dfrac {t^2} 6 \end{cases} \

$-\infin < t < \infin$