Question

Which is the equation of a circle that is centered at the origin?O (– 1)2 + (y – 1)2 = 4O2? + (y - 1)2 = 2O 2 + y2 = 7Ox+y=8

Answer 1

`x^2+y^2\text{ = 7 (option C)}`

Step-by-step explanation:

Standard equation of circle:

`(x-h)^2+(y-k)^2=r^2`
`\begin{gathered} \text{If centered at the origin:} \\ (h,\text{ k) = (0, 0)} \\ h\text{ = 0, k = 0} \end{gathered}`
`\begin{gathered} \text{The equation of circle becomes:} \\ (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}`

comparing the above equation with the options given:

`\begin{gathered} x^2+y^2=7\text{ has the form} \\ x^2+y^2=r^2,wherer^2\text{= }7 \end{gathered}`
`x^2+y^2\text{ = 7 (option C)}`