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Write the equation in standard form for the circle $x^2+y^2-16= 0$ .

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Convert equations of circles from general to standard form

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Q. Write the equation in standard form for the circle

x^2+y^2-16= 0

.

Identify equation and goal: Identify the given equation and the goal. $\newline$ The given equation is $x^2 + y^2 - 16 = 0$ . We need to write this equation in the standard form of a circle, which is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is the radius.
Move constant term: Move the constant term to the other side of the equation. $\newline$ To get the equation in standard form, we need to isolate the terms with $x$ and $y$ on one side and move the constant to the other side. We do this by adding $16$ to both sides of the equation. $\newline$ $x^2 + y^2 - 16 + 16 = 0 + 16$ $\newline$ This simplifies to: $\newline$ $x^2 + y^2 = 16$
Verify standard form: Verify the standard form of the circle. $\newline$ The equation $x^2 + y^2 = 16$ is now in the standard form of a circle with a center at $(0, 0)$ and a radius of $4$ , since $16$ is the square of $4$ .

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