Question

If $A(2, 4)$ and $B(6, 10)$ are two fixed points and if a point $P$ moves so that $\angle APB$ is always a right angle, then the locus of $P$ is:

• A. $x^2 + y^2 + 8x + 14y + 52 = 0$
• B. $x^2 + y^2 - 8x + 14y - 52 = 0$
• C. $x^2 + y^2 + 8x - 14y + 52 = 0$
• D. $x^2 + y^2 - 8x - 14y - 52 = 0$
• E. $x^2 + y^2 - 8x - 14y + 52 = 0$

Hint:

Alternatively, you can use the slope condition: $m_{AP} \times m_{BP} = -1$. This results in $\frac{y-4}{x-2} \times \frac{y-10}{x-6} = -1$, which leads to the same diameter form equation.

Answer 1

Answer: (E)