Question

Write an equation of the circle given its center and radius

Answer 1

x²+y² = 16

Explanation:

We have given the center and radius of a circle.

Center = (0,0) ; Radius = 4

We have to find the equation of the circle.

The standard equation for the circle is:

(x-h)²+(y-k)²= r² where (h,k) is the center of circle and r is the radius of circle.

Putting given values in above equation , we have

(x-0)²+(y-0)²= (4)²

(x)²+(y)² = 16

x²+y² = 16 which is the equation of circle.

Answer 2

`16=(x-0)^(2)+(x-0)^(2)`

Explanation:

In writing equations for circles with the center and radius given we follow the formula
`r^(2)=(x-h)^(2)+(y-k)^(2)`.

The value of h and k are the center values of (0,0).

So we have:

h = 0

k = 0

r = 4

Now let's plug these values into our formula.

`4^(2)=(x-h)^(2)+(x-k)^(2)`

`4^(2)=(x-0)^(2)+(x-0)^(2)`

`16=(x-0)^(2)+(x-0)^(2)`