Angle between the parabola y^2=4(x-1) and x^2+4(y-3)=0 at the common end of their latus rectum is

Step-by-step solution

Determine the angle between the parabolas at their intersection point. The parabolas are y^2 = 4(x-1) and x^2 = -4(y-3) , with their latus rectum endpoints determined by their respective focus coordinates. For the parabola y^2 = 4(x-1) , the vertex is (1,0) and the focus is (2,0) , giving latus rectum ends at (2,2) and (2,-2) . For x^2 = -4(y-3) , the vertex is (0,3) and the focus is (0,2) ; ends of the latus rectum correspond to x = 2 , y=2 , resulting in endpoints of (2,2) and (-2,2) . The common point is (2,2) .