Question

Let A(5, 12), B(- 13cosθ, 13sinθ) and C(13sinθ, 13cosθ) where θ is real be the vertices of  ΔABC. Then, the orthocentre of ΔABC lies on the line

(A)  x - y - 7 = 0

(B)  x +y 7 = 0

(C)  x -  y + 7 = 0

(D)   x + y + 7 + 0

Answer 1

Correct option  (c)  x - y + 7 = 0

Explanation :

Observe that B and C are image of each each other on the line y = x and hence the side BC varies and is perpendicular to the line y = x. Hence, the orthocentre lies on the altitude through A(5, 12) and parallel to the line y = x, whose equation is

y - 12 = 1(x - 5)

x - y + 7 = 0