Question

The relation between $p$ and $q$ such that the point $(p,q)$ is equidistant from $(-4,0)$ and $(4,0)$ is

• A. $p=0$
• B. $q=0$
• C. $p+q=0$
• D. $p+q=8$

Answer 1

The correct option is A $p=0$

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Since, $A(p,q)$ is equidistant from $B(-4,0)$ & $C(4,0)$

$AB=AC$

$AB=\sqrt{(p+4{)}^2+q^2}=$

$AC=\sqrt{(p-4{)}^2+q^2}$

$(p+4{)}^2+q^2=(p-4{)}^2+q^2$

$16p=0$

$p=0$