I am working on a long problem and the solution i am getting differs from the answer in the textbook.
It boils down to completing the square. The method i use works in the first half of the problem but the book gets a different answer in the 2nd half. Basically for the coordinates of the centre of a circle my x coordinate is correct, but my y coordinate is incorrect.
Can somebody complete the square on the following and give me coordinates for the centre of the circle. My answer is (x=0.5, y=-0.5). The book gives the y as -1.
The expression is: 4x^2+4y^2-4x+8y-11=0.
My solution has : y^2+2y becomes y^2+y+0.25 (b=0.5)= (y+0.5)^2-0.25 Mr F says: Expand this out. Do you get y^2 + 2y? The book is correct. Go back and review how to complete the square. Or perhaps, by expanding the book's answer, you will see why it is has to be correct ....
The book has: y^2+2y becomes (y+1)^2-1