QuestionSolve $x^{2}+y^{2}=81$ for $y$ . Find the positive and negative functions: $y_{1}=\square$ , $y_{2}=\square$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is a circle equation in the form $x^{}+y^{}=r^{}$ , where $r$ is the radius of the circle. . We need to solve this equation for $y$ in terms of $x$ to get two explicit functions, $y_{1}$ and $y_{}$ .

STEP 2

Start by isolating $y$ in the given equation.
$y^{2} =81 - x^{2}$

STEP 3

Take the square root of both sides to solve for $y$ . Remember that the square root of a number can be either positive or negative.
$y = \pm \sqrt{81 - x^{2}}$

STEP 4

Now we can write down the two explicit functions. The positive square root gives us the first function, $y_{1}$ , and the negative square root gives us the second function, $y_{2}$ .
$y_{1} = \sqrt{81 - x^{2}}$ $y_{2} = -\sqrt{81 - x^{2}}$ So, the two explicit functions are $y_{1} = \sqrt{81 - x^{2}}$ and $y_{2} = -\sqrt{81 - x^{2}}$ .

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