Explain briefly why

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Explain briefly why, for the hyperbola

\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1

whose foci are at

(\pm c,0)

, the three quantities

a, b

and

c

satisfy the relation

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