A circle with centre C has equation x^2 + y^2 + 2x - 6y - 40 = 0. Express as (x - a)^2 + (y - b)^2 = d.

First we must complete the square on both x and y. To complete a square we must take the number before the x and half it, for example nx we get n/2. We then write it as (x + n/2)- (n/2)2

So for our question we have 2x so we will write (x + 1)2 - (1)2. Then we repeat for y. We have -6y so we will write (y - 3)2 - (3)2.

We then write all of this together as (x + 1)2 - 1 + (y - 3)2 - 9 - 40 = 0. Rearrange and we get (x + 1)+ (y - 3)2  = 50

Reuben M. 13 plus  Maths tutor, GCSE Maths tutor, A Level Maths tutor...

4 months ago

Answered by Reuben, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£18 /hr

Lucy W.

Degree: Conservation Biology and Ecology (Masters) - Exeter University

Subjects offered: Maths, Science+ 4 more

Extended Project Qualification

“Hello! My name's Lucy, and I'm a first year student at Exeter university, studying for aMSci in Conservation Biology and Ecology. I've always had a love and fascination for the outdoors and the world around me, and as I learnt more t...”

£30 /hr

Adam D.

Degree: Economics and Management (Bachelors) - Bristol University

Subjects offered: Maths, Economics


“I am a second year undergraduate student at the University of Bristol, studying Economics and Management. I achieved A* in Economics and Maths A-levels and an A* at maths GCSE so would be very happy to help any students who are studyi...”

£18 /hr

Visitation L.

Degree: Biomedical sciences (Bachelors) - Durham University

Subjects offered: Maths, Biology


“Hi, I am Visitation, a second year Biomedical scientist at Durham. Science and Maths are such fascinating subjects and I would like to share my passion and help you through my tutorials!”

About the author

£18 /hr

Reuben M.

Degree: Maths (Masters) - York University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About Me I am a maths student at University of York. I have had a love for maths and all it's complexity ever since I was little and I aspire to make others love maths as I do. I am a qualified basketball coach and have been teaching...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Express 0.545454... as a fraction in its simplest form.

Find the solutions of the equation x^2 - 2x - 8 =0

How many people chose A?

Factorise and solve x^2 - 8x + 15 = 0

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss