The area (in sq. units) of the region
A = {(x, y) : |x| + |y| $$ \le $$ 1, 2y² $$ \ge $$ |x|}

The general solution of the differential equation

$$\sqrt {1 + {x^2} + {y^2} + {x^2}{y^2}} $$ + xy$${{dy} \over {dx}}$$ = 0 is :

(where C is a constant of integration)

The region represented by
{z = x + iy $$ \in $$ C : |z| – Re(z) $$ \le $$ 1} is also given by the
inequality : {z = x + iy $$ \in $$ C : |z| – Re(z) $$ \le $$ 1}

Let a , b, c , d and p be any non zero distinct real numbers such that
(a² + b² + c²)p² – 2(ab + bc + cd)p + (b² + c² + d²) = 0. Then :