# How do you find all points that have an x -coordinate of –4 and whose distance from point (4, 2) is 10?

How do you find all points that have an x -coordinate of –4 and whose distance from point (4, 2) is 10?
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Quenchingof
We want D=10
Let $\left({x}_{1},{y}_{1}\right)$ be $\left(4,2\right)$
Let $\left({x}_{2},{y}_{2}\right)$ be $\left(-4,{y}_{2}\right)$
$10=\sqrt[2]{{\left(4-\left(-4\right)\right)}^{2}+{\left(2-{y}_{2}\right)}^{2}}$
Squaring both sides we have
${\left(10=\sqrt[2]{{\left(4-\left(-4\right)\right)}^{2}+{\left(2-{y}_{2}\right)}^{2}}\right)}^{2}$
$⇒100=\left({8}^{2}\right)+{\left(2-{y}_{2}\right)}^{2}$
$⇒100=64+\left(4-4{y}_{2}+{\left({y}_{2}\right)}^{2}\right)$
$⇒{\left({y}_{2}\right)}^{2}+4{y}_{2}+4=36$
$⇒{\left({y}_{2}\right)}^{2}+4{y}_{2}-32=0$
$⇒\left({y}_{2}+8\right)\left({y}_{2}-4\right)=0$
y_2 = -8; 4