Question

i have to eliminate the parameter and obtain the standard form of the rectangular equation of x=h+rcos(theta), y=k+rsin(theta)

Answer 1

$$
x=h+rcos(\theta) \implies cos(\theta)=\cfrac{{(x-h)}^2}{r^2}\\
y=k+rsin(\theta) \implies sin(\theta)=\cfrac{{(y-k)}^2}{r^2}\\
\text{now keeping in mind the pythagorean identity } cos(\theta)^2+sin(\theta)^2=1\\
\cfrac{(x-h)^2}{r^2}+\cfrac{(y-k)^2}{r^2}=1
$$

Answer 2

$$
x=h+rcos(\theta) \implies implies cos(\theta)=\cfrac{{(x-h)}}{r}\\
y=k+rsin(\theta) \implies sin(\theta)=\cfrac{{(y-k)}}{r}\\
\text{now keeping in mind the pythagorean identity } cos(\theta)^2+sin(\theta)^2=1\\
\cfrac{(x-h)^2}{r^2}+\cfrac{(y-k)^2}{r^2}=1
$$
there, better :)