QuestionThe sum of the squares of $x$ and $y$ equals 8: $x^{2}+y^{2}=8$ .

Studdy Solution

STEP 1

Assumptions1. The equation is in the form of a circle equation $x^{}+y^{}=r^{}$ , where $r$ is the radius of the circle. . The variables $x$ and $y$ represent coordinates on a plane.
3. The equation represents all points $(x, y)$ that are a distance $r$ from the origin.

STEP 2

Identify the radius of the circle from the equation. In the given equation, $x^{2}+y^{2}=8$ , the radius $r$ is the square root of the constant term on the right side of the equation.
$r = \sqrt{8}$

STEP 3

Calculate the radius.
$r = \sqrt{8} \approx2.83$

STEP 4

Translate the equation into a sentence using the calculated radius and the understanding of what the equation represents.
The sentence translation of the equation $x^{2}+y^{2}=8$ is"The equation represents all points (x, y) that are approximately2.83 units away from the origin on a plane."

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