Question

what is analytical geonetry

Answer 1

basically it is the geometry that is based on algebra. Here, for instance, we don't so much analyse circles as figures in space, but with equations on Cartesian coordinates. \[r^2=x^2+y^2\] is a circle in analytic geometry.\[1={x^2\over a^2}+{y^2\over b^2}\] is an ellipse
\[1={x^2\over a^2}-{y^2\over b^2}\] is a hyperbola