The combination of two arcs was written in a later edit. The result should be a complete ellipse matching your parameters. Move to P, do an arc with the parameters I just described to point Q, and another arc back to P. All these terms refer to the description in the SVG 1.1 specification. 0), and the sweep flag arbitrarily but equal for the two halfs of the ellipse (e.g. The transverse magnication of the image (compared to the object) is the ratio of the image. Set the large-arc flag any way you like (e.g. focal point, an input ray through the center of the lens emerges at the same angle, and an input ray that passes through the front focal point emerges parallel to the optical axis. You can compute the rotation from the slope of the line connecting the foci, using atan2 or similar, and use that as the third parameter instead of 100. Once you have the lengths of the semimajor and semiminor axis, you can use these as the radii arguments to the arc command of an svg path, which are the first two parameters, 180,50 in your example. So if F and G are your focal points, then you have P = ( f − a)/(2 f) × F + ( f + a)/(2 f) × G as one point on the ellipse, and Q = ( f + a)/(2 f) × F + ( f - a)/(2 f) × G as the other. It's easiest to choose these on the major axis. You'll also need to compute two points on the ellipse. Notice that f still refers to half the distance between the focal points. From that you get b = sqrt(1.3 2 - 1) f ≈ 0.83 f. Now that you have included the 130% part in your question, I can give you a computation for that as well.
![focalpoint 1.1 focalpoint 1.1](https://cdn.xxl.thumbs.canstockphoto.fr/sac-type-sanguine-o-vecteur-eps_csp18696145.jpg)
Then you get the length of the semiminor axis as b = sqrt( a 2 - f 2), where 2 f is the distance between your foci. So for example, if you have one point which should lie on the ellipse, then you could compute the distance to the two foci, add those lengths, and know that sum to be equal to 2 a, where a is the length of the semimajor axis. Given one more parameter and the distance between the foci, you can compute all other parameters like the lengths of the semimajor and semiminor axis, as you require them for your path specification.
![focalpoint 1.1 focalpoint 1.1](https://image.slidesharecdn.com/contrastfocalpointexercise-150925183738-lva1-app6892/95/contrast-amp-focal-point-exercise-4-638.jpg)
one point on the ellipse, or something similar.
![focalpoint 1.1 focalpoint 1.1](https://i.pinimg.com/736x/e0/3a/11/e03a11c879c41e723630fd9831d964a1--hallway-lighting-ceiling-medallions.jpg)
This can be seen from the fact that one can draw an ellipse by wrapping a string of fixed length around the focal points and keeping it taunt with the drawing pen. The two focal points by themselves do not define an ellipse, you'll need one more real parameter.