Line intersecting spheroid I have two planes $(A): u_{1}x + v_{1}y + w_{1}z = d_{1}$ and $(B): u_{2}x + v_{2}y + w_{2}z = d_{2}$.
They intersect together, then they yield a line $(L)$ that has a direction vector $M (x_{M},y_{M},z_{M})$
$M$ is the cross product of the normal vectors of $A$ and $B$
$M = (u_{1},v_{1},w_{1})×(u_{2},v_{2},w_{2})$
The parametric equations of the line $L$ of a parameter $t$  are:
$x = x_{P} + x_{M}.t$
$y = y_{P} + y_{M}.t$
$z = t$
I intersect this line $L$ with an spheroid $E$ of semi-axis major $a$ in the equatorial plane $xoy-Plane$  along $x-axis$ and $y-axis$ and semi-axis minor $b$ along $z-axis$
My problem is how to find the coordinates of the two points of intersection?

$(x_p, y_p, z_p)$ is any point on the line of intersection. 
For example, suppose the two planes are x+ 2y+ z= 1 and 2x- y+ z= 3.  Subtracting the first equation from the second gives x- 3y= 2 so x= 3y+ 2.  Taking, arbitrarily, y= 0, x= 2.  Then both 2+ 0+ z= 1 and 4- 0+ z= 3 give z= -1. (2, 0, -1) is one of the infinitely many points on the line of intersection. 
