Question

Find a polar equation for the curve represented by the given Cartesian equation:
a) 5x+2y=5

Write the answer in the form r=f(t) where t stands for θ. Find r

b) x2−y2=3

Write the answer in the form r2=f(t) where t stands for θ. Find r^2

Answer 1

For polar coordinates we have
\[x=rcos(\theta)\]
\[y = rsin(\theta)\]\[r = \sqrt{x^2+y^2}\]

Answer 2

\[5x+2y=5 \implies 5(rcos(\theta)+2rsin(\theta))=5\] now mess around with it, and see what you get :-)

Answer 3

i don't know how to solve further can you help?

Answer 4

Each term contains an r,
try factoring! :)

Answer 5

cos()+1/2sin() =r but wasn't right

Answer 6

I don't understand what you did...
where are the 5's?

\(\large\rm 5r\cos\theta+2r\sin\theta=5\)
Factor out an r from each term,
\(\large\rm r(5\cos\theta+2\sin\theta)=5\)
Then just divide both sides by that big bracketed thing, ya?

Answer 7

cos(t)+5/2sin(t) ?

Answer 8

still wasn't right

Answer 9

?? 0_o

Answer 10

\[\large\rm r(stuff)=5\qquad\to\qquad r=\frac{5}{stuff}\]

Answer 11

The division should be simple, I think maybe you're over complicating it :O

Answer 12

Zeps right, you're just one step away from completing it :P

Answer 13

(5/5cos(t))+(5/2sint) is what i put but it wasn't right

Answer 14

\[r = \frac{ 5 }{ (5 \cos \theta+2\sin \theta) }\] let theta = t

Answer 15

you can't split it into two fractions like that nick.

Answer 16

\[\large\rm \frac{a}{b+c}\ne\frac{a}{b}+\frac{a}{c}\]

Answer 17

oh okay thanks