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**danthemaths****Member**- Registered: 2012-10-18
- Posts: 2

I have a question saying "Hence find the coordinates of the point C such that AC is a diameter of this circle".

I already know:

Points: A(0,2) B(4,-2)

Equation of line AB: x^2+y^2-2x+2y=8 => and simplify that you get: (x-1)^2+(y+1)^2=10

Perpendicular Equation to line AB (through B): y=-x+2

I do not know how to work this out! Could you please explain to me step by step if u can on how to solve this?

Thanks in advance

Dan

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi Dan,

Welcome to the forum.

How much was given in this question?

Just points A and B is not enough to fix one circle, so I'll assume you were told the equation as well.

So (1,-1) is the centre of the circle. Let's call it O.

Then from A to O is the same as from O to C. (as you want AOC to be a straight line and diameter.)

That's enough to just count across and down from A to O and hence find C without needing perpendicular lines.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

Hi danthemaths;

First you should always have a drawing to help you think about the question and also to pose it for others.

Perpendicular Equation to line AB (through B): y=-x+2

Although it does not matter I am not getting that equation for the perpendicular.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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