Help with the centre of a circle, (a,b) rule

Hi guys, finding myself getting tripped up as to the centre of the circle C(a,b) rule.

Let me use the following example.
Find the equation of the circle centre C(1,-2) and passing through the point A (4,7).

Using the (x-a)²+(y-b)² notation, this gives us (4-1)² +(7-(-2))²

I guess what I am confused by is how exactly we came about with those values being placed. Why was it in that form, as opposed to say (1-4) (-2-7)? Does it matter what order they go in?

Reply 1

moment of truth

19

Really speaking due to the values being squared it wouldn't make a difference because it will be positive anyway.

Reply 2

User947387

OP

17

Ok.....I had noticed that :smile:

What am I am wondering is, would the position of the values matter in any of the other equations? Such as calculating the equation of the circle, or the tangent of a circle etc etc

Reply 3

tombayes

12

Original post by apronedsamurai

Hi guys, finding myself getting tripped up as to the centre of the circle C(a,b) rule.

Let me use the following example.
Find the equation of the circle centre C(1,-2) and passing through the point A (4,7).

Using the (x-a)²+(y-b)² notation, this gives us (4-1)² +(7-(-2))²

I guess what I am confused by is how exactly we came about with those values being placed. Why was it in that form, as opposed to say (1-4) (-2-7)? Does it matter what order they go in?

What is your question exactly?

This is what you did:

The equation of your orginal circle is:

(x-1)^2+(y+2)^2=r^2

since it goes though the point (4,7) this gives

r^2=90

so the equation of the circle is

(x-1)^2+(y+2)^2=90

.

So now changing the points gives a different equation.

(edited 9 years ago)

Reply 4

Pratonium

Exactly, the whole points of the tangent co-ordinates is to substitute them into the equation (x-1)^2+(y+2)^2=r^2 and find what radius squared is, the tangent points are not part of the equation thus the final equation is (x-1)^2+(y+2)^2=90