Consider a plane curve defined as the locus of a point P such that ∣PF2−PF1∣ is a fixed positive real number, where the fixed points (foci) are F1(−c,0) and F2(c,0).
Answer the following questions with brief explanations.
a. (i) Define the curve described above.
b. (ii) Give a geometric argument to explain why the fixed difference ∣PF2−PF1∣ equals the distance between the two vertices of the curve.
c. (iii) If the fixed difference equals 12 cm, state the distance between the vertices of the curve.