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# Circle Co-Ordinate Geometry. watch

1. Hi I'm studying from home so sometimes there are parts that my course omits from teaching me, at which point I defer to the internet, so hi!

My question is referring to circles. Particularly the questions of the format:

1) Write down the radius and the co-ordinates to the centre of:

a) x2 + y2 + 3x - 5y + 2 = 0

These I am fine with however I am stuck when the x2 and y2 terms are given coefficients,
This is the exact question I am stuck on:

b) 3x2 + 3y2 + 6x - 4y - 15 = 0

Thank you
2. (Original post by Bysteven)
Hi I'm studying from home so sometimes there are parts that my course omits from teaching me, at which point I defer to the internet, so hi!

My question is referring to circles. Particularly the questions of the format:

1) Write down the radius and the co-ordinates to the centre of:

a) x2 + y2 + 3x - 5y + 2 = 0

These I am fine with however I am stuck when the x2 and y2 terms are given coefficients,
This is the exact question I am stuck on:

b) 3x2 + 3y2 + 6x - 4y - 15 = 0

Thank you
Try dividing the equation by 3
3. (Original post by Bysteven)
...
The coefficients of and will always be the same on circles questions so notnek's method is guaranteed to work every time.
4. (Original post by Mr M)
The coefficients of and will always be the same on circles questions so notnek's method is guaranteed to work every time.
Thanks guys, I divided by 3 however my answer for the radius differs from the given answer at the back of the book.
My answer was 7 25/36 the textbook is saying 1/3√58.

Here is how I got there:

- 3x2 + 3y2 + 6x - 4y - 15 = 0

- x2 + 3x + y2 - 4/3 y - 5 = 0

- (x + 1.5)2 + (y - 4/6)2 - 2.25 - 16/36 - 5 = 0

- (x + 1.5)2 + (y - 2/3)2 = 7.25 + 8/18 ( or 7 + 1/4 + 8/18)

- (x + 1.5)2 + (y - 2/3)2 = √ (7 50/72) or √ (7 25/36)

The Co-ordinates are right at (-1,2/3) but can someone please explain how I got the radius wrong.

Thank you!
5. (Original post by Bysteven)
Thanks guys, I divided by 3 however my answer for the radius differs from the given answer at the back of the book.
My answer was 7 25/36 the textbook is saying 1/3√58.

Here is how I got there:

- 3x2 + 3y2 + 6x - 4y - 15 = 0

- x2 + 3x + y2 - 4/3 y - 5 = 0

- (x + 1.5)2 + (y - 4/6)2 - 2.25 - 16/36 - 5 = 0

- (x + 1.5)2 + (y - 2/3)2 = 7.25 + 8/18 ( or 7 + 1/4 + 8/18)

- (x + 1.5)2 + (y - 2/3)2 = √ (7 50/72) or √ (7 25/36)

The Co-ordinates are right at (-1,2/3) but can someone please explain how I got the radius wrong.

Thank you!
6x divided by 3 is 2x NOT 3x!!
6. (Original post by brianeverit)
6x divided by 3 is 2x NOT 3x!!
Thanks I can't believe I missed that,
In which case,

- 3x2 + 3y2 + 6x - 4y - 15 = 0

- x2 + 2x + y2 - 4/3 y - 5 = 0

- (x + 1)2 + (y - 4/6)2 - 1 - 16/36 - 5 = 0

- (x + 1)2 + (y - 2/3)2 = 6 16/36

- (x + 1)2 + (y - 2/3)2 = √ 6 4/9

Is this what everyone else would have solved it at? In which case I am still off the final answer.
Thanks so much for all the help
7. (Original post by Bysteven)
Thanks I can't believe I missed that,
In which case,

- 3x2 + 3y2 + 6x - 4y - 15 = 0

- x2 + 2x + y2 - 4/3 y - 5 = 0

- (x + 1)2 + (y - 4/6)2 - 1 - 16/36 - 5 = 0

- (x + 1)2 + (y - 2/3)2 = 6 16/36

- (x + 1)2 + (y - 2/3)2 = √ 6 4/9

Is this what everyone else would have solved it at? In which case I am still off the final answer.
Thanks so much for all the help
Actually I've just worked it out that 1/3 √58 AND √6 4/9 are both equal to 2.53859 which means I have got the correct answer

Would I still get the mark or would it have to match the format of the given answer?
8. (Original post by Bysteven)
Actually I've just worked it out that 1/3 √58 AND √6 4/9 are both equal to 2.53859 which means I have got the correct answer

Would I still get the mark or would it have to match the format of the given answer?
Exact form is fine.
9. (Original post by Bysteven)
Actually I've just worked it out that 1/3 √58 AND √6 4/9 are both equal to 2.53859 which means I have got the correct answer

Would I still get the mark or would it have to match the format of the given answer?
You must be careful with your notation , writing it is not clear that the fraction is included in the square root. Writing as an improper fraction, i.e. is much better and we then have as required
10. Gotcha thanks alot this helped loads )

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