Question

For each quadratic, list the center and radius, then graph each circles (f) 4x + 4y? - 16x + 24y = -27 enter: (b) x + y2 - 4x = 0 (d) x + y2 - 2x - 8y = 8 2 (h) x + y? - 7y=0 ( ) x + y? - 2ax + 2by =c

Answer 1

To find the radius and center of the circle:

`x^2+y^2-4x=0`

we need to complete the squares in the x variable:

`\begin{gathered} x^2+y^2-4x=0 \\ (x^2-4x)+y^2=0 \\ (x^2-4x+(-2)^2)+y^2=(-2)^2 \\ (x-2)^2+y^2=4 \end{gathered}`

Therefore the center is the point (2,0) and the radius is 2.

The graph of the circle is: