Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2012-11-10 21:52:00

danthemaths
Novice

Offline

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

## #2 2012-11-10 22:23:01

bob bundy
Moderator

Offline

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

## #3 2012-11-10 22:33:26

bobbym

Online

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.