Mathematics

Problem

For the two fixed points

F_{1}(-4,0)

and

F_{2}(4,0)

on the x–axis, a point

P(1,3)

is considered. a. (i) Calculate the distances

PF_{1}

and

PF_{2}

separately. b. (ii) Find the value of

PF_{1}+PF_{2}

and hence determine the length of the major axis of the ellipse that passes through

P

with

F_{1},F_{2}

as its foci. c. (iii) Verify, by direct substitution, that

P

satisfies the standard equation of this ellipse.