Question

How do you find $a$ and $b$ of a Hyperbola?

Answer 1

Hyperbola:

Equation of hyperbola is given by:

${\left(\frac{x-h}{a}\right)}^2-{\left(\frac{y-k}{b}\right)}^2=1$

$=\frac{{(x-h)}^2}{a^2}-\frac{{(y-k)}^2}{b^2}=1$ ……($a$)

For eg:

$\frac{{(x-3)}^2}{16}-\frac{{(y-5)}^2}{9}=1$ …($b$)

Compare both the equation you will get

$$\begin{gathered} a^2=16,b^2=9 \\ a=4,b=3 \end{gathered}$$

Hence, this way we can find the $a\&b$of a hyperbola.