The area of the triangle formed by the lines joining the vertex of the parabola x^2=20 y to the end of its Latus rectum is

Step-by-step solution

For the parabola x^2 = 20y , comparison with the standard form x^2 = 4ay yields 4a = 20 , so a = 5 . The vertex is at the origin: V = (0, 0) . The latus rectum lies along y = a = 5 . Substituting into the equation gives x^2 = 100 , so x = 10 . The endpoints are L₁ = (-10, 5) and L₂ = (10, 5) . The triangle formed by these points has base length 20 and height 5. Its area is 1 2 20 5 = 50 .