If the area (in sq. units) of the triangle formed by the intersection of a line parallel to the x -axis and passing through the point P ( h , k ) with the line y = x and x + y = 2 is 4 h 2 , then the locus of the point P is

Step-by-step solution

Here, the triangle formed by a line parallel to the x -axis and passing through P   ( h ,   k ) and the straight line y = x and y = 2 - x is shown below. Since, area of Δ ABC = 4 h 2 ∴ 1 2 · AB · AC = 4 h 2 Where AB = 2 k - 1 and AC = 2 k - 1 ⇒ 1 2 · 2 k - 1 2 = 4 h 2 ⇒ 4 h 2 = k - 1 2 ⇒ 2 h = ± k - 1 Hence, the locus of the point P is 2 x = ± y - 1