Let X = x , y ∈ ℤ × ℤ : x 2 8 + y 2 20 < 1 and y 2 < 5 x . Three distinct point P , Q and R are randomly chosen from X . Then the probability that P , Q and R form a triangle whose area is a positive integer, is

Step-by-step solution

Given, Equation of ellipse x 2 8 + y 2 20 = 1 And equation of parabola   y 2 = 5 x Now intersection point of ellipse and parabola will be 2 , 10   &   2 , - 10 Now plotting the region x 2 8 + y 2 20 < 1   and   y 2 < 5 x we get, Now randomly chosen points will be between origin and the intersecting point, So, the integer points inside region are 2 ,   1 ,   2 ,   - 1 ,   2 ,   2 ,   2 ,   - 2 , 2 ,   3 ,   2 ,   - 3 , 2 ,