distance from origin to vertex; area; tangent line

wow, thanks a lot for pointing that out. Yeah, that's a typo. I'm trying to find the x-intercept of the tangent line & express it in terms of b.
I'll go edit that now.

At first, I used the equation of a circle & plugged in 0 for y. That left me with +/-2b. However, I don't think that would be the x-intercept of a tangent line & concluded that I thought I was on the wrong track.
So then I thought that maybe if I used that technique & found the y-intercept, I would have the point that the tangent line has the touch & maybe I could go from there.
I'm not sure if I'm on the right track, but I'm trying to look at it from a bunch of different angles & see what I could possibly do.
Anyway, I came up with -b^2 - root(2b^2 + b^4) as the y-intercept, but I'm still not really sure how/if that helps.
 
V(b, -b^2)

r^2 = b^2 + b^4

Equation of circle

(x - b)^2 + (y+b^2)^2 = b^2 + b^4

y intercept (x =0) of the circle

y = 0 or -2b^2

So the smaller y-intercept is (0,-2b^2).

Now continue ....

refer to the drawing made by galactus - carefully....
 
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