Answer
The distance of a point $P\left( x,y \right)$ from the origin in terms of the point’s $x\text{-coordinate}$ is, $d=\sqrt{{{x}^{4}}-15{{x}^{2}}+64}$
Work Step by Step
The distance of a point $P\left( x,y \right)$ from the origin is
$\begin{align}
& d=\sqrt{{{\left( x-0 \right)}^{2}}+{{\left( y-0 \right)}^{2}}} \\
& =\sqrt{{{x}^{2}}+{{y}^{2}}}
\end{align}$
Substitute ${{x}^{2}}-8$ for $y$ in the above equation
$d=\sqrt{{{x}^{2}}+{{\left( {{x}^{2}}-8 \right)}^{2}}}$
Use the formula ${{\left( A-B \right)}^{2}}={{A}^{2}}-2AB+{{B}^{2}}$ in the above equation
$\begin{align}
& d=\sqrt{{{x}^{2}}+{{x}^{4}}-16{{x}^{2}}+64} \\
& =\sqrt{{{x}^{4}}-15{{x}^{2}}+64}
\end{align}$
The required distance of a point $P\left( x,y \right)$ from the origin in terms of the point’s $x\text{-coordinate}$ is, $d=\sqrt{{{x}^{4}}-15{{x}^{2}}+64}$.
