Question

quadratic, list the center and radius, then graph each circle lah (b) x2 + y2 - 4x = 0 (d) x2 + y2 - 2x - 8y = 8 (f) 4x2 + 4y2 - 16x + (h) x2 + y2 - 7y = 0 (1) x2 + y2 - 2ax + 2by = c 4y2 - 16x + 24y = -27

Answer 1

Given the equation of circle b;

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

We need to express the above equation in the form;

`(x-h)^2+(y-k)^2=r^2`

where;

`\begin{gathered} r=\text{radius of the circle} \\ (h,k)=\text{ coordinate of the center of the circle} \end{gathered}`

Solving for h,k and r;

`\begin{gathered} x^2+y^2-4x=0 \\ x^2-4x+y^2=0 \\ \text{add 4 to both sides;} \\ x^2-4x+4+y^2=0+4 \\ (x-2)^2+(y-0)^2=4 \\ (x-2)^2+(y-0)^2=2^2 \\ So; \\ h=2 \\ k=0 \\ r=2 \end{gathered}`