(a) State the necessary and sufficient algebraic conditions that a general…
MATHEMATICS · Subjective · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
(a) State the necessary and sufficient algebraic conditions that a general second–degree equation in x and y must satisfy in order to represent a circle.
(b) Consider the quadratic equation
4x2+4y2+6x−8y+5=0.
(i) Test whether this equation satisfies the conditions stated in part (a).
(ii) Give a clear reason for your conclusion.
(c) Explain, with reference to the coefficients, why the presence of a non–zero xy term would prevent a second–degree equation from representing a circle.