## Precalculus (6th Edition) Blitzer

The distance of a point $P\left( x,y \right)$ from the origin in terms of the point’s $x\text{-coordinate}$ is, $d=\sqrt{{{x}^{4}}-7{{x}^{2}}+16}$
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 ${{x}^{2}}-4$ for $y$ in the above equation $d=\sqrt{{{x}^{2}}+{{\left( {{x}^{2}}-4 \right)}^{2}}}$ 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}}-8{{x}^{2}}+16} \\ & =\sqrt{{{x}^{4}}-7{{x}^{2}}+16} \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, $d=\sqrt{{{x}^{4}}-7{{x}^{2}}+16}$