Question

Find $a$ if the distance between $(a,2)$ and $(3,4)$ is $8$.

• A. $3\pm \sqrt{60}$
• B. $4\pm \sqrt{60}$
• C. $3\pm \sqrt{6}$
• D. None of these

Answer 1

The correct option is A $3\pm \sqrt{60}$

By square of distance formual:

$8^2=(3-a{)}^2+(4-2{)}^2$

$\Rightarrow 64=a^2-6a+13$

$\Rightarrow a^2-6a-51=0$

solving the quadratic by quadratic formula, we get:

$a=(3+\sqrt{(}60)$ or $(3-\sqrt{(}60))$.