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C2 Question - Co Ord Geom watch

1. A tangent to the circle, drawn from the point P(8, 17) touches the circle (x - 4)^2 + (y - 5)^2 = 25 at T.

What is the method to do this? How do I find out the co ords of T?

Thanks.
2. Work out the gradient of the line which goes from the centre of the circle to the point P. This line will be perpendicular to your tangent. It might be good if you draw this problem.
3. I've worked out the gradient of centre to P as 3. So perpendicular gradient is -1/3.

Then the eq of the line perpendicular going through P is:

y = -1/3x + 59/3

What do I do next?
4. (Original post by Matt_2K)
A tangent to the circle, drawn from the point P(8, 17) touches the circle (x - 4)^2 + (y - 5)^2 = 25 at T.

What is the method to do this? How do I find out the co ords of T?

Thanks.
So you have a circle with centre (4,5) and radius 5. (The radius isn't that important here).
Always draw a rough sketch of what's happening. ie roughly where the circle is and where P is. Then everything is easier. It doesn't have to accurate.

You've found the gradient from the centre of the circle to P.
The line joining the centre of the circle to T will be perpendicular to the line from the centre to P.
You have the gradient of this line which goes through T and the centre to be -1/3.
You can find the equation of this line by using y=mx+c. So m=-1/3, you can find c by putting in the coordinates of the centre because you know that the line goes through this point.
Then substitute y=mx+c into the circle equation to find x. Then you can find y.

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