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Problem 722

Write the equation of the circle with center $$\mathrm{C}$$ at the origin and with radius 7 .

Expert verified
The equation of the circle with center at the origin and radius 7 is $$x^2 + y^2 = 49$$.
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Step 1: Circle Equation Formula

The equation of a circle with center at the origin $$(0,0)$$ and radius $$r$$ is given by the equation: $x^2 + y^2 = r^2.$

Step 2: Substitute Radius Value

Given the radius of the circle as 7, substitute the value into the equation: $(x^2 + y^2) = 7^2.$

Step 3: Simplify the Equation

Simplify the equation to get the final equation of the circle: $x^2 + y^2 = 49.$ Thus, the equation of the circle with center at the origin and radius 7 is $$x^2 + y^2 = 49$$.

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