Find the point at which the two intersect

Limits, differentiation, related rates, integration, trig integrals, etc.

Find the point at which the two intersect

Postby lilrockerboi66 on Wed Jul 16, 2014 12:39 am

Please this is kind of tricky, but I need to find the point at which the parabola y=x^2 and a unit circle traveling on the x axis from the right intersect.
I know that in order to do this I need to use the distance formula, finding the minimum distance between the point of intersection and the center of the circle. We do not know the point for the center of the circle except for the y value of 1.

[*]The circle stops at the point of intersection with y=x^2
Last edited by lilrockerboi66 on Wed Jul 16, 2014 1:13 am, edited 1 time in total.
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Postby stapel_eliz on Wed Jul 16, 2014 1:07 am

lilrockerboi66 wrote:I need to find the point at which the parabola y=x^2 and a unit circle traveling on the x axis from the right intersect.

What do you mean by "traveling on the x axis"? If the circle is moving (and, for a while, passing through the parabola), how can there be "the [one] point" of intersection?

Please be complete. Thank you! :wink:
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Re: Find the point at which the two intersect

Postby lilrockerboi66 on Wed Jul 16, 2014 1:09 am

It stops at the parabola and intersects it at a point. Say it was rolling and it stopped when it hit y=x^2. Hope that clears it up a bit.
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Postby stapel_eliz on Wed Jul 16, 2014 10:53 am

lilrockerboi66 wrote:It stops at the parabola and intersects it at a point. Say it was rolling and it stopped when it hit y=x^2.

So the circle was "rolling"... with its center on the x-axis? with its "bottom" on the x-axis?

When you reply, please include a clear listing of everything you have tried so far. Also, the full and exact text of the exercise would be very helpful. Thank you! :wink:
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Re: Find the point at which the two intersect

Postby lilrockerboi66 on Wed Jul 16, 2014 9:48 pm

Its bottom is on the x axis. I don't have text, it's a bonus problem. I have no idea how to figure out the x value of the middle of the circle. That's all I need to do the rest of the problem and find the point of intersection.
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Re: Find the point at which the two intersect

Postby theshadow on Thu Jul 17, 2014 1:43 am

The slope of the tangent (where the circle touches the parabola) has to be 2x (since its coming from the right). If the intersection is at (a, a^2) then the slope of the tangent is 2a and the slope of the radius there is -1/(2a). The center is (h, k) = (h, 1). The distance between the center and the intersection is 1.

Do the Distance Formula and the slope formula. I can get a value for a. What do you get?
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