The foci of a curve are F1(−5,0) and F2(5,0). A student claims that the point P(7,4) lies on the hyperbola whose transverse axis is the x-axis and whose constant difference of focal distances is 8 units.
Answer the following questions to verify the student’s claim:
(i) State the exact numerical condition that any point (x,y) must satisfy, in terms of PF1 and PF2, in order to lie on this hyperbola.
(ii) Calculate the value of ∣PF2−PF1∣ for the point P(7,4).
(iii) Using the value obtained in part (ii), decide whether P(7,4) lies on the given hyperbola. Give a brief justification based on your calculation.