I'm trying to solve the following excersice:
Given the following equations, represent by a vector function:
- $y=x^2+1$ from $(3,10)$ to $(-1,2)$
- $y=4-x$ with $x\in [-2,3]$
- ${x^2\over{25}} + {y^2\over{16}} =1$ counter-clock wise from $(5,0)$
So, parameterizing, in each case with $x = t$
- $y=t^2+1$, then $r_1=(t,t^2+1)$
- $y=4-t$, then $r_2(t)=(t, 4-t)$
- ${t^2\over{25}} + {y^2\over{16}} = 1 \implies y=\sqrt{16-{16\over{25}}t^2}$, then $r_3 =\left(t, \sqrt{16-{16\over{25}}t^2}\right)$
My question is: this is well done?, and what can I do with data on which the domain is defined (i.e. "from $(3,10)$ to $(-1,2)$")?
Thanks!