Conic Sections in MPT

I was tutoring a student about the general geometry of conic sections (circles, parabolas, ellipses and hyperbolas) and was wondering if this can be applied in an actuarial or quantitative framework. According to ChatGPT, it can. Modern portfolio theory (MPT) states that the return (mu) relative to the risk (sigma) can be plotted in the form of a hyperbola/parabola (parabola if plotted against the variance of the portfolio). ChatGPT also states that two highly correlated assets can be modeled as an ellipse. I found this interesting because if that’s true, how can I use the property of conic sections to maximize the performance of a portfolio? If the utility/budget constraints can be modeled as a straight line, can I use the properties of general geometry to maximize return and minimize risk?