Question

Let $A(5,12),B(-13cos\theta ,13sin\theta )$ and $C(13sin\theta ,-13cos\theta )$ be vertices of $\Delta ABC$ where $\theta ϵR$. The locus of orthocenter of $\Delta ABC$ is

• A. x – y + 7 = 0
• B. x – y - 7 = 0
• C. x + y - 7 = 0
• D. x + y + 7 = 0

Answer 1

The correct option is A x – y + 7 = 0

$A(5,12),B(-13cos\theta ,13sin\theta ),C(13sin\theta ,-13cos\theta )$
$m_{BC}=-1$
$\therefore$ Equation of altitude from A
$(y–12)=x-5$
$x-y+7=0$