How do you identify the center and radius of the circle ${(x - 1)}^{2} + y^{2} = 10$ $(x-1)^2+y^2=10$ ?

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Answer 1 · 2018-04-07T21:56:51

Center: $(1, 0)$ $(1,0)$ Radius: $\sqrt{10}$ $sqrt10$

The standard equation of a circle with center $(h, k)$ $(h,k)$ and radius $r$ $r$ is

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x-h)^2+(y-k)^2=r^2$

Examining

${(x - 1)}^{2} + y^{2} = 10,$ $(x-1)^2+y^2=10,$

we see we really just have

${(x - 1)}^{2} + {(y - 0)}^{2} = 10^{2}$ $(x-1)^2+(y-0)^2=10^2$ , making the center

$(1, 0)$ $(1, 0)$ and the radius $r^{2} = 10 \to r = \sqrt{10}$ $r^2=10 -> r=sqrt10$

How do you identify the center and radius of the circle (x−1)2+y2=10(x-1)^2+y^2=10?