Question

find two functions defined implicitly by this equation.
$(x + 5)^2 + (y - 6)^2 = 20$
$y = pmsqrt{? - (x + quad)^2 + quad}$

Explanation:

Step1: Start with the given equation

We have the equation \((x + 5)^2+(y - 6)^2 = 20\). Our goal is to solve for \(y\) in terms of \(x\).

Step2: Isolate the \((y - 6)^2\) term

Subtract \((x + 5)^2\) from both sides of the equation:
\[
(y - 6)^2=20-(x + 5)^2
\]

Step3: Take the square root of both sides

Take the square root of both sides to solve for \(y - 6\). Remember that when we take the square root, we get both a positive and a negative root:
\[
y - 6=\pm\sqrt{20-(x + 5)^2}
\]

Step4: Solve for \(y\)

Add 6 to both sides of the equation to isolate \(y\):
\[
y=\pm\sqrt{20-(x + 5)^2}+6
\]

Answer:

The values in the boxes are \(20\), \(5\), and \(6\) respectively. So the equation is \(y=\pm\sqrt{20-(x + 5)^2}+6\)