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If I have been given the centre of a circle, say (2,-3) and also the radius, say, 6 units, how would I find a tangent point of that circle? i.e. How do I find a particular point on that diameter of the circle?

Thank you braintic!!!! Great answer, helped me! :D

Some of you might remember this from New Senior Maths 2U. The question is: Find the equation of the locus that is subject to: the distance of a point from the line x=4 is equal to the distance from the line y=1. The second question: Find the equation of the locus from the line...