Question

4x^2+9y^2 = 16
Convert to polar equation and make graph. Confused.

Answer 1

I'd like to know what the real solution to that previous problem was.

Answer 2

http://www.wolframalpha.com/input/?i=r%3D4%2Fsqrt%284%2B5sin%5E2%28theta%29%29

when i follow my gut I get this

convert x^2 and y^2 to their respective r^2cos^2(t) and r^2sin^2(t)

factor out the r^2 and algebra it into submission

Answer 3

converting to sin^2(t) was arbitrary, I could have gone with cos^2(t) as well, or left it all intact

Answer 4

\[4x^2+9y^2 = 16\]\[\frac{4x^2}{16}+\frac{9y^2}{16} = 1\]\[\frac{x^2}{4}+\frac{y^2}{16/9} = 1\]\[\left(\frac{x}{2}\right)^2+\left(\frac{y}{4/3}\right)^2 =1\]\[x=2\cos\phi\quad,\quad y=\frac{4}{3}\sin\phi\quad;\quad 0\leq\phi\leq 2\pi\]

Answer 5

Thanks!!!