 Intersection of a prolate spheroid and a concentric sphere

For the prolate spheroid $u^2/a^2+(v^2+w^2)/b^2=1$ with $a>b>0$, intersect the concentric sphere $u^2+v^2+w^2=R^2$. When $b<R<a$, subtraction gives two circles in the perpendicular planesTheir centers lie on the long principal axis and the line through the centers is normal to both planes. At $R=b$ the circles merge into the equator; at $R=a$ they shrink to the two polar vertices. There is no intersection for $R<b$ or $R>a$.