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## #1 2012-11-09 22:52:00

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".

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?

Dan

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## #2 2012-11-09 23:23:01

bob bundy
Registered: 2010-06-20
Posts: 8,508

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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Bundy

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## #3 2012-11-09 23:33:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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