Parameterizing the Witch of Agnesi Curve

[dnylander]

whitch of agnesi problem) its a curve defined as follows. let O be the origin, let T be the point (0,1), and let m be the line through T parallel to the x-axis. Let C be the circle centered at (0,0.5) with radius 0.5. For any point P on the circle besides O and T, we draw a ray from O through P. let this ray intersex m at point X. we then draw the altitude from X to the line through P parallel to the x-axis. The foot of this altitude, point A, is on the witch curve. When we trace out the resulting points A for all possible P, and include point T, we get the witch curve. Find the Parameterization for it and a function f such that the witch curve is the graph of the function y = f(x)

Thanks SO SO much

 

[Mark44]

Please don't double post.

 

[dnylander]

Sorry mark I'm new

 

[dnylander]

Please post a response if you get the chance. I'm sorry I double posted- I promise I won't do it again. (that's not an excuse to not answer my question haha)

 

[sutupidmath]

Please post a response if you get the chance. I'm sorry I double posted- I promise I won't do it again. (that's not an excuse to not answer my question haha)

One of the rules of PF is that you have to post your attempt at the solution before anyone here can provide any hints.

 

[dnylander]

please verify my solution:

a= radius
x= 2acos(t)
y= a[1-cos 2(t)]
y= 8a^3/x^2+4a^2

Thanks