Answer to Question #225810 in Analytic Geometry for Bless

Question

Write down the parametric coordinates of any point on each of the following parabolas.

(a) y² = 8x

b) y² = 24x

c) y² = -16x

d) x² = 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} \$$

$$-\infin < t < \infin$$