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1. -RM-
2. (Original post by UCASLord)
There are two circles, Z and M. Circle Z has the equation (x - 1)^2 + (y - 1)^2 = 1, and circle M has the equation (x - 5)^2 + (y - 7)^2 = 9. Find the points that are the nearest to each other on both circles.

I've worked out the distance from the center of Z to M, which is √54, and the gradient from the center of Z to the center of M is 3/2.

I know I somehow need to apply the gradient to Z, and in reverse to M, to find the points that lie on the line ZM (center to center), which also lie on the edges of the circles. However, I haven't managed to find a way to do this.

One option is to find the equation of the line through the centres and then solve simultaneous equations to find the points where this line intersects the circles.

A quicker option is to use vectors.
3. -RM-
4. (Original post by UCASLord)
I quickly worked this out for the (x - 1)^2 + (y - 1)^2 = 1 circle, and got x = 1 + 213/13, so from there y = 3/2(1 + 213/13) - 1/2... Would those be the right coordinates for the the point on the circle Z?
That's correct. Don't forget to simplify the y value.

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