Question 963974
What is y= x^2 + 1 in polar form
<pre>
When changing from rectangular form (or vice-versa), always
draw this firs:

{{{drawing(500/3,200,-1,4,-1,5,
line(-5,0,7,0), line(0,-3,0,7),line(0,0,3,4),line(3,4,3,0),
red(arc(0,0,2,-2,0,54)), locate(1.5,0,x), locate(3.1,2,y),
locate(.8,2,r),locate(.4,.5,theta)


 )}}}

The idea is to get rid of the letters x and the y and end
up with an equation that has only r and &#952; in it.

{{{y}}}{{{""=""}}}{{{x^2 + 1}}}

Write what we know about the sine and cosine:

{{{sin(theta)=y/r}}},  solve for y, get {{{y=r*sin(theta)}}}

{{{cos(theta)=x/r}}},  solve for x, get {{{y=r*sin(theta)}}} 

Substitute in

{{{y}}}{{{""=""}}}{{{x^2 + 1}}}

{{{r*sin(theta)}}}{{{""=""}}}{{{(r^""*cos(theta))^2 + 1}}}

or

{{{r*sin(theta)}}}{{{""=""}}}{{{r^2cos^2(theta) + 1}}}

Edwin</pre>