Mathematics

Problem

While deriving the standard equation of an ellipse, the identity

b^{2}=a^{2}-c^{2}

is introduced. What is the chief purpose of bringing this identity into the algebraic steps? a) To maintain dimensional consistency of the algebraic steps b) To express the eccentricity

e

solely in terms of

a

and

b

c) To replace

c

so that the equation no longer contains the focal distance d) To relate the semi-minor axis

b

directly to

c

for later substitution

Browse the problem library