Coordinate Geometry

Geometry Level 3

Normals are drawn to the ellipse $x^{2/5} + y^{2/4} = 1$ that are inclined at $45^\circ$ to the $x$ -axis. What are the points of intersection of two of these normals?

(0,1/3) and (0,-1/2*3^0.5) (-1/3,0) and (1/2*3^0.5 , 0) (0,1/3) and (-1/3,0)