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hb2325
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Homework Statement
Ok so this is a question from last years past paper of my course:
X= 1/2 intersects the circle that is centered at origin at two points, one of which is in the lower half plane y<0; what is the equation of the tangent tot the same circle at this point?
Homework Equations
So basically x = 1/2 intersects the circle twice, so the points at which it intersects would have co-ordinates 1/2, y and I would use these to find radius to find the gradient of the x = tangent.
But so far I have been unable to find a value for the raidus or the point y where the circle intersects x = 1/2.
I have gotten ansers with respect to y but can not find the value of it and hence I am stuck
The Attempt at a Solution
forumla of the circle = X^2 + y^2 = r^2
so r^2 = 1/4 + y^2
Then i try to find the gradient of radius (0,0) to (1/2, y) which is 2y so the radius of the gradient of the tangent line is -1/2y but what is y :S am i missing something very obvious here? Please help.
Thank you.
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