A conic C satisfies the differential equation (1+y2)dx−xydy=0 and passes through the point (1,0). An ellipse E which is confocal with C has its eccentricity equal to 32. Find the locus of the point of intersection of the perpendicular tangents to the ellipse E.
a. x2+y2=4
b. x2+y2=8
c. x2+y2=10
d. x2+y2=13