Question

If P(3, 4), Q(-7, 6). The point A on x-axis for which PA + AQ is least at

• A. (-2, 0)
• B. (-1, 0)
• C. (3, 0)
• D. (2, 0)

Answer 1

Answer: (B)

(-1, 0)

Let A be (x, 0)
$PA+A\theta =\sqrt{(x-3{)}^2+16}+\sqrt{(x+7{)}^2+36}$
$\frac{d\left(d\right)}{dx}=\frac{(x-3)}{\sqrt{(x-3{)}^2+16}}+\frac{(x+7)}{\sqrt{(x+7{)}^2+36}}$
$(x-3{)}^2((x+7{)}^2+36)=(x+7{)}^2((x-3{)}^2+16)$
$6(x-3)=\pm 4(x+7)$
$x=-1,23$