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r=sqrt(x^(2)+y^(2))
The equation gives the quantity
r in terms of the quantities
x and
y. Which of the following equations gives a possible value of
x in terms of
r and
y ?

$r=\sqrt{x^{2}+y^{2}}$ $\newline$ The equation gives the quantity $r$ in terms of the quantities $x$ and $y$ . Which of the following equations gives a possible value of $x$ in terms of $r$ and $y$ ?

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Find the vertex of the transformed function

Full solution

Q.

r=\sqrt{x^{2}+y^{2}}

\newline

The equation gives the quantity

r

in terms of the quantities

x

and

y

. Which of the following equations gives a possible value of

x

in terms of

r

and

y

?

Given Equation: We start with the given equation: $r = \sqrt{x^2 + y^2}$ .
Square Both Sides: Square both sides to get rid of the square root: $r^2 = x^2 + y^2$ .
Isolate $x^2$ : Subtract $y^2$ from both sides to isolate $x^2$ : $r^2 - y^2 = x^2$ .
Solve for x: Take the square root of both sides to solve for x: $x = \pm\sqrt{r^2 - y^2}$ .

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