The point P on a circle is transformed into the point P' on a ellipse.
The point P is (6,8), and lies on a circle with the equation X^2 + Y^2 = 100.
Point P' lies on the same graph after it has been transformed into a ellipse, with the co-ordinates (4,12). (No transitions, only a stretch factor change.) Both conics have an origin of 0,0. Find the equation for the new ellipse in the form, x^2 / a^2 + y^2 / b^2 = 1. Most importantly find the stretch factors A and B.
standard circle = x^2 + y^2 = r^2
standard ellipse = x^2 / a^2 + y^2 / b^2 = 1.
The Attempt at a Solution
Till this point, I have only done this type of question when the points being transformed lied on either the major or minor axis. I have attempted to substitute the point in which the ellipse passes through, but to no avail, as I cannot solve for both A and B at the same time as they're both unknown. I have thought about linear systems, but I only have one pair of co-ordinates, and I don't believe I can figure out the major/minor axis given my level of trigonometry (only works on circles). I am unable to identity the relationship between P and P' and its relevance to helping me find A and B.