In order to simplify a circle equation, you need to first break up the x's and y's: x^2 + 10x + ... + y^2 + 4y + ... + 11 = 0 The '...' are the constants that we need to add in, to be able to factorise our x and y statements. To find those constants, we divide the coefficient of our variable by 2 and then square it e.g. the first ... will be (10/2)^2 = 25 and the second will be (2/2)^2 = 4 so we have: x^2 + 10x + 25 + y^2 + 4y + 4 + 11 = 0 So far, this is actually an ILLEGAL operation. We have magically added a 25 and a 4 to the LHS of our equation, meaning that this is not the same as what we started with. In order to make this legal, we must also add the 25 and 4 to the RHS, effectively meaning we have added 0 to our equation (not changed anything) so we have: x^2 + 10x + 25 + y^2 + 4y + 4 + 11 = 25 + 4 Now we can factorise and simplify: (x+5)^2 + (y+2)^2 = 25 + 4 - 11 And referring to the circle equation, the constants on the right hand side are = r^2 so: r^2 = 5^2 + 2^2 - 11 r = sqrt(5^2 +2^2 -11)

thank you that makes a lot of sense

You probably found the equation of the circle from part a I’m guessing just sqrt the right side ( because equation of circle is (x-a)^2 +(y-b)^2 =r^2)so you get 3root2

thank you that makes sense

You have to complete the square on the x^2-10x and y^2+4y, this gives you the 25 and the 4

thank you that makes sense

which paper is this?