Let A 3 a , a , a > 0 , be a fixed point in the x y -plane. The image of A in y -axis be B and the image of B in x -axis be C . If D 3 cos θ , a sin θ , is a point in the fourth quadrant such that the maximum area of ∆ A C D is 12 square units, then a is equal to _____

Step-by-step solution

A = 3 a , a B = - 3 a , a is the image of A on y-axis C = - 3 a , - a is the image of B in x-axis D 3 cos θ , a sin θ Area of triangle A C D will be 1 2 3 a a 1 - 3 a - a 1 3 cos θ a sin θ 1 = 3 a cos θ - sin θ The maximum area of triangle is 3 a 2 i.e. 3 a 2 = 12 ⇒ a = 8