Question

I NEED HELP!!!

convert the rectangular equation to a polar equation that expresses r in terms of theta

x^2=16y

r=?

Answer 1

Note, \[x=rcos \theta \]
\[y = rsin \theta \] then we have \[r=\sqrt{x^2+y^2}\]

Answer 2

@mollykenney does it make sense? :)

Answer 3

so we have sqrt of x^2 + (-16)y = r?

Answer 4

The question wants you to convert this x^2=16y to polar equations. @Astrophysics already gave you what you need to know.

Answer 5

x^2=16y into polar coordinates and then from there you solve for r. When you convert it to polar coordinates, you will get r and theta as your new variables. Solve for r.

Answer 6

what does x equal to and y equal to in polar coordinates?

Answer 7

i don't know @Zale101 can we take it step by step I'm really confused with this concept

Answer 8

Would you agree, if \[x=rcos \theta \] then \[x^2 = r^2\cos^2 \theta \]

Answer 9

What would \[16y = ?\]

Answer 10

quick and dirty: \(x=r\cos\theta, y=r\sin\theta\), then
\(16x^2 = y \iff 16 r^2\cos^2\theta = r\sin\theta\iff r(16r\cos^2\theta - \sin\theta)=0\)
\(\iff r=0 \text{ or } r=\frac{\sin\theta}{16\cos^2\theta} \)
So it's the relation \(r = \frac{\sin\theta}{16\cos^2\theta} \), \(\theta\in[0,\pi]\setminus\{\pi/2\}\).