Point(s) of intersection between a conic and a line, and between two conics in homogeneous coordinates.
1 2  intersectConicLine(C, l)
intersectConicConic(C1,C2)

C, C1, C2 
(3 \times 3) matrix representation of conics. 
l 
a (3 \times 3) vector of the homogeneous representation of a line. 
The homogeneous coordinates of the intersection points. If there are two points of intersection, it returns a (3 \times 2) matrix whose columns correspond to the homogeneous coordinates of the intersection points. If there is only one point, a (3 \times 1) vector of the homogeneous coordinates of the intersection point is returned. If there is no intersection, NULL
is returned.
RichterGebert, Jürgen (2011). Perspectives on Projective Geometry  A Guided Tour Through Real and Complex Geometry, Springer, Berlin, ISBN: 9783642172854
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  # Ellipse with semiaxes a=8, b=2, centered in (0,0), with orientation angle = pi/3
C < ellipseToConicMatrix(c(8,2),c(0,0),pi/3)
# Ellipse with semiaxes a=5, b=2, centered in (1,2), with orientation angle = pi/5
C2 < ellipseToConicMatrix(c(5,2),c(1,2),pi/5)
# line
l < c(0.25,0.85,3)
# intersection conic C with line l:
p_Cl < intersectConicLine(C,l)
# intersection conic C with conic C2
p_CC2 < intersectConicConic(C,C2)
# plot
plot(ellipse(c(8,2),c(0,0),pi/3),type="l",asp=1)
lines(ellipse(c(5,2),c(1,2),pi/5), col="blue")
addLine(l,col="red")
points(t(p_Cl), pch=20,col="red")
points(t(p_CC2), pch=20,col="blue")

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