Find the equation of the tangent - Please help trying for 2 hours now.

[hb2325]

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

formula 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.

 

[HallsofIvy]

There exist an infinite number of circles with center at the origin. There exist an infinite number of points at which the line x= 1/2 crosses those circles. There are an infinite number of answers to this question depending on the radius of the circle. If you are not given the radius of the circle, you cannot give a specific answer.

 

[hb2325]

Now that you said it, you're right, can't believe I did not see it earlier, I will just leave my anser in the form of y saying it depends on y.

Thanks a lot for the prompt and helpful reply :)

 

[HallsofIvy]

I think I would be more inclined to leave it in terms of r, the radius of the circle. Of course, if r< 1/2, there is no point of intersection.