<p>Geometric problems involving conics and quadrics have been studied in great detail due to their scientific and engineering significance. Problems, such as the computation of proximity to a given point or the projection of a point onto a conic and quadric, are known to be identical in geometry. It is, perhaps, not so well known that these problems are also algebraically analogous to the concurrence of three conics or quadrics at a point and the tangency of two coplanar conics etc. In this article, nine problems involving conics and quadrics are studied, primarily to demonstrate that many of these are geometrically equivalent while all of them are amenable to the same algebraic solution procedure involving multivariate resultants. The mathematical formulations presented are illustrated via representative examples. Symbolic computation techniques are used to obtain a univariate polynomial of degree up to 8 with its coefficients in the closed form in all the cases, establishing the analytical nature of the uniform solution process. This symbolic treatment is shown to be effective in solving the general algebraic problem without the need for any prior characterisation of the quadrics. The theoretical derivations are illustrated via numerical examples, and the results are visualised graphically.</p>