C2-circle graphs.

OP

Original post by Maz A

The formula for the equation of a circle is given by:

(x-a)^2 + (y-b)^2=r^2

a and b being the x and y co ordinates of the centre of a circle respectively. TO find the co ordinates try to draw a nice diagram out. You have the radius and a point it touches meaning that you can use pythagoras's theorem to work out the distance, better still put the values into the equation (from he point) and it will give you the centre.

Isn't distance = radius ?

Reply 3

thefatone

6

Original post by Questioness

Isn't distance = radius ?

yes

well radius²

Reply 4

The OP knows the radius is 10; she is asking what to do from there.

OP, look at your sketch, what can you say about the line segments?

Reply 5

OP

Original post by Zacken

The OP knows the radius is 10; she is asking what to do from there.

OP, look at your sketch, what can you say about the line segments?

Makes one long line joined by the two circles?

Reply 6

Original post by Questioness

Makes one long line joined by the two circles?

Joined by *what* of the two circles?

What is the length of that line? Can you maybe form some sort of useful triangle from that line by using the known centre?

Reply 7

OP

Original post by Zacken

Joined by *what* of the two circles?

What is the length of that line? Can you maybe form some sort of useful triangle from that line by using the known centre?

Yup, don't really see how Pythagoras is gunna find the centre though. Carry on :redface:

Length of the Line=radius so therefore 10.

Reply 8

Original post by Questioness

Yup, don't really see how Pythagoras is gunna find the centre though. Carry on :redface:

Length of the Line=radius so therefore 10.

Are you the length of the line is 10?

Reply 9

OP

Original post by Zacken

Are you the length of the line is 10?

Ohh, I see. Initially, I drew it like this, why is it wrong?

Pictured it at a bad angle sorry. You'll need to tilt it

(edited 7 years ago)

Reply 10

Original post by Questioness

Ohh, I see. Initially, I drew it like this, why is it wrong?

That's fine, it's just that the triangle isn't of much use - whereas, in this:

You can then easily find the angle theta since you know the length of the green line (4-1) and the length of the horizontal black line to the green line (6-2).

Then

\sin \theta = \frac{3}{5}

and

\cos \theta = \frac{4}{5}

.

Then, you also know that

\sin \theta = \frac{3}{5} = \frac{a}{15}

So

a = 9

but that's the length of the vertical black line, so you gotta add something to it, blah blah, can you see the method and do it for yourself?

Reply 11

OP

Original post by Zacken

That's fine, it's just that the triangle isn't of much use - whereas, in this:

You can then easily find the angle theta since you know the length of the green line (4-1) and the length of the horizontal black line to the green line (6-2).

Then

\sin \theta = \frac{3}{5}

and

\cos \theta = \frac{4}{5}

.

Then, you also know that

\sin \theta = \frac{3}{5} = \frac{a}{15}

So

a = 9

but that's the length of the vertical black line, so you gotta add something to it, blah blah, can you see the method and do it for yourself?

I got it. Thanks :h:

Reply 12

Original post by Questioness

I got it. Thanks :h:

No problem - can't believe it took me such a long time to spot the method. Glad you got it. :smile:

Reply 13

OP

Yea, I'm stuck on another question :frown:

.

Tried using this method
https://m.youtube.com/watch?v=VZFeyS76euI
But non the the midpoints for the y axis match the answer.

Attachment not found

Answer is (-2,2)

Original post by Questioness

Yea, I'm stuck on another question :frown:

.

Tried using this method
https://m.youtube.com/watch?v=VZFeyS76euI
But non the the midpoints for the y axis match the answer.

Attachment not found

Answer is (-2,2)

You've found the midpoints - now find the equation of two perpendicular bisectors (one for AB and one for AC) and then equate them to each other to find where they intersect (which is the centre).

Which is precisely what the video says to do, are you sure you've watched the video? :tongue:

(edited 7 years ago)

Reply 15

OP

Original post by Zacken

You've found the midpoints - now find the equation of two perpendicular bisectors (one for AB and one for AC) and then equate them to each other to find where they intersect (which is the centre).

Which is precisely what the video says to do, are you sure you've watched the video? :tongue:

Yeah, I have issues.
Thanks again XD

Reply 16