Equation of Hyperbola in Reduced Form/Cartesian Frame/Proof 2

Theorem

Let $K$ be a hyperbola such that:

the transverse axis of $K$ has length $2 a$

the conjugate axis of $K$ has length $2 b$.

Let $K$ be aligned in a cartesian plane in reduced form.

$K$ can be expressed by the equation:

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

Proof

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Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {V}$. The Hyperbola: $2$.