Question

This circle is centered at the origin, and the length of its radius is 8. what is the equation of the circle?

Answer 1

hello : 
note : 

an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =0    b = 0     r =8
the equation of the circle is : x²+y² = 64

Answer 2

Answer:  The required equation of the circle is $x^2+y^2=64.$

Step-by-step explanation:  We are given to find the equation of a circle with center at the origin and radius of length 8 units.

We know that

the equation of a circle with center at the point (g, h) and radius of length r units is given by

$(x-g)^2+(y-h)^2=r^2.$

Here,

center, (g, h) = (0, 0) and radius, r = 8 units.

Therefore, the equation of the circle will be

$(x-0)^2+(y-0)^2=8^2\\\\\Rightarrow x^2+y^2=64.$

Thus, the required equation of the circle is $x^2+y^2=64.$