I'm a bit confused with your work.
First of all, find the equation in the $xy$ plane then substitute the $r\sin\theta$ and $r\cos\theta$ eqns
Question is incomplete
If $2,3,5,7,19|a$ then $lcm(2,3,5,7,19)=3990|a$. So just $3990*1$ and $3990*2$.
Use the fact that $dist=2a\sqrt{1-\frac{b^2}{a^2}}$ and $a,b$ are given in the equation.
Wow nice.
$f(-2)+g(-2)=4+\frac{1}{4}=\frac{17}{4}$
$f(2)+g(2)=4+4=8$
By definition, $f(2)=f(-2)$ & $g(-2)=-g(2)$. So sub $f(2)=f(-2)=x$ and $g(-2)=-g(2)=y$.
Then $x+y=\frac{17}{4}$ and $x-y=8$. Adding the two, $2x=\frac{49}{4}$ hence $x=f(2)=\frac{49}{8}$.
It's super easy once you use the divisibility rule for 11 and note that the digits must all be relatively high ($\frac{40}{5}=8$ is the average)
It's a depressed cubic equation. I would recommend multiplying both sides by 1000 and either using rational root theorem or using cardano's formula.
wolframalpha.com is also helpful
You set it equal to zero and factor:
$$\left(\frac{x-3}{5}-\frac{y+1}{2}\right)\left(\frac{x-3}{5}+\frac{y+1}{2}\right)=0$$
So one or the other is zero. Solve both of them then pick the one with positive slope w.r.t x
You just plug! Here's a start: $g(5)=5+8=13$ and $f(5)=5^2+2\cdot 5+5=25+10+5=40$.
$5n+24+4n+30=180\implies 9n+54=180\implies n=14$
you can finish
