## anonymous one year ago 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

1. Astrophysics

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

2. Astrophysics

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

3. anonymous

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

4. zepdrix

Each term contains an r, try factoring! :)

5. anonymous

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

6. zepdrix

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?

7. anonymous

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

8. anonymous

still wasn't right

9. zepdrix

?? 0_o

10. zepdrix

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

11. zepdrix

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

12. Astrophysics

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

13. anonymous

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

14. Astrophysics

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

15. zepdrix

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

16. zepdrix

$\large\rm \frac{a}{b+c}\ne\frac{a}{b}+\frac{a}{c}$

17. anonymous

oh okay thanks

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