1. ## Circles and co-ordinates

Hey

Prove that the line y=2x is a tangent to the circle x^2 + y^2 - 8x -y +5=0
and find the coordinates of the point of contact.

Can somebody please help, I am just really confused with what to do and where to start.

THANKS

2. First, find out where the line and circle intersect. It should be a single point. Next, prove that a second line going from the center of the circle to the intersection point is perpendicular to the line y=2x. That is a non-calculus method, which I'm assuming is your desired approach.

3. ## Thanks

Thanks, that's brilliant.

4. Originally Posted by mathdeity
First, find out where the line and circle intersect. It should be a single point. Next, prove that a second line going from the center of the circle to the intersection point is perpendicular to the line y=2x. That is a non-calculus method, which I'm assuming is your desired approach.
Actually, for the case of a circle, intersection at one point is sufficient to guarantee that the line is a tangent.

-Dan