Convert the polar equation r^2(1+2sin^2theta)=4 to an equation with Cartesian (rectangular) coordinates

Question

dumbcow · Answer

Note:
x = r*cos(theta)
y = r*sin(theta)
x^2 +y^2 = r^2

--> r^2 + 2r^2 sin^2 = 4
--> (x^2 +y^2) +2y^2 = 4
-->x^2 +3y^2 = 4

looks like an ellipse

anonymous · Answer

solution from book said x^2 + (y+1)^2=5

anonymous · Answer

I think dumbcow is right...

anonymous · Answer

according to your solution your center is at (0,-1) but mathematica has it at (0, 0)

anonymous · Answer

yea i trust dumbcow

anonymous · Answer

thanks guys

dumbcow · Answer

welcome, the solution doesn't match
are you sure the question is typed correctly

anonymous · Answer

the solution is wack lots of mistakes in it lol

dumbcow · Answer

haha ok
well i double checked on wolfram and i am correct

anonymous · Answer

one more thing...
x^2 + (y+1)^2=5
is actually a cirlce with radius sqrt5

anonymous · Answer

does wolfram teaches how to do it? or you just look at the graph and can tell right away

dumbcow · Answer

no not that i know of

i just compared the graphs

dumbcow · Answer

http://www.wolframalpha.com/input/?i=r^2%281%2B2sin^2%28theta%29%29+%3D4 http://www.wolframalpha.com/input/?i=x^2+%2B3y^2+%3D4

anonymous · Answer

thanks have a good night!