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What is the radius of this circle?

Leam with an example $\newline$ What is the radius of this circle?

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Find the radius or diameter of a circle

Full solution

Q. Leam with an example

\newline

What is the radius of this circle?

Identify Equation: Step $1$ : Identify the equation of the circle and compare it to the standard form. $\newline$ The given equation is $x^2 + y^2 = 36$ . The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center and $r$ is the radius. Here, it looks like $h = 0$ and $k = 0$ , so the equation simplifies to $x^2 + y^2 = r^2$ .
Solve for $r^2$ : Step $2$ : Solve for $r^2$ . $\newline$ From the equation $x^2 + y^2 = 36$ , we can see that $r^2 = 36$ .
Find Radius: Step $3$ : Find the radius $r$ by taking the square root of $r^2$ . Taking the square root of both sides, we get $r = \sqrt{36}$ . This gives $r = \pm 6$ .
Determine Value: Step $4$ : Determine the appropriate value for the radius. $\newline$ Since a radius cannot be negative, we discard $-6$ . Therefore, the radius of the circle is $6$ .

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