Question

How do I find the center & radius, then write a standard equation for a,b, and c?

Answer 1

Firstly , we will locate centres and radius in the figures

(a)

We can see that

centre=(h,k)=(0,0)

radius=r=5

now, we can use standard equation of circle

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

we can plug values

we get

`(x-0)^2+(y-0)^2=5^2`

`x^2+y^2=25`

(b)

We can see that

centre=(h,k)=(5,4)

radius=r=3

now, we can use standard equation of circle

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

we can plug values

we get

`(x-5)^2+(y-4)^2=3^2`

`(x-5)^2+(y-4)^2=9`

(c)

We can see that

centre=(h,k)=(4,3)

radius=r=5

now, we can use standard equation of circle

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

we can plug values

we get

`(x-4)^2+(y-3)^2=5^2`

`(x-4)^2+(y-3)^2=25`