Question

Explain how you would graph the following set of parametric equations by plotting points and describing the orientation.

Answer 1

Answer with explanation:

The given parametric equation in , t ,

x = 3 t, y=t²

$t=\frac{x}{3}\\\\t^2=[\frac{x}{3}]^2\\\\y=\frac{x^2}{9}\rightarrow x^2=9 y$

,represents the curve parabola, having Axis in positive Direction of ,Y axis.

⇒⇒For, t=0

x=0, y=0

for, t=1

x=3, y=1

for, t=2

x=6, y=4

.............

...............

we will get different set of ordered pairs for different integral values of t.

Vertex =(0,0)

Axis (Orientation): Y axis.

Focus: Comparing with general equation of parabola , x²=4 a y,gives focus

 $\rightarrow4 a=9\\\\a=\frac{9}{4}\\\\\text{focus}=(0,\frac{9}{4})$

Equation of Directrix:

    $y=\frac{-9}{4}$

Answer 2

Concept:

First eliminate the t from x=3t and then put it in y=t² and then graph it. As, limit of t is not  restricted so t ∈ R(all real numbers)

As it is difficult to make graph here so I have solved it by hand and add all detail regarding it.