The area of a triangle formed by the lines joining the vertex of the parabola x^2= y to the ends of its latus rectum is 18 sq units then the value of is

Step-by-step solution

The equation of the parabola is x^2 = y . Comparing this with the standard form x^2 = 4ay , we have 4a = , which implies a = 4 . The vertex of the parabola is at (0, 0) . The ends of the latus rectum are at (2a, a) and (-2a, a) . Substituting a = 4 , the coordinates are ( 2 , 4 ) and (- 2 , 4 ) . The triangle is formed by the vertices (0, 0) , ( 2 , 4 ) , and (- 2 , 4 ) . The area of a triangle with vertices (x₁, y₁) , (x₂, y₂) , and (x₃, y₃) is given by 1 2 |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)| . Substituting