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Find an equation of the circle with center at origin and radius $4$.

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Answer:

$x^2 + y^2 = 16$

Step by Step Explanation:

1. The equation of a circle with center at $(a, b)$ and radius $r$ is given by
   $(x - a)^2 + (y - b)^2 = r^2$
2. Given:
   Center of the circle is at center $i.e(0,0)$
   Radius of the circle $= 4$
   $\implies a = 0, b = 0,$ and $r = 4$
3. Therefore, the equation of the circle is given by
   $(x - 0)^2 + (y - 0)^2 = 4^2 \\ \implies x^2 + y^2 = 16$
   Hence, the required equation is $x^2 + y^2 = 16$.

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