... ( ) SP ′ = ePM ′ = e CN CZ ] ′ = e x e ex = ... ( ) Hence, SP S P + ′ = a ex ex = Remark When b , the equation ( h , becomes ( h the equation of circle with centre ( , ) h k and radius a . When b a e .
Hence the eccentricity of the circle is zero . Furthere, SP PM = implies PM →∞ . That is, the directrix of the circle is at infinity. Remark Auxiliary circle or circumcircle is the circle with length of major axis as diameter and Incircle is the circle with length of minor axis as diameter.
They are given by x and x respectively.