Geometry: Hyperbolas I was wondering how would I complete the square for this particular hyperbola?
$4x^2 - 5y^2 + 24y = 16$
I tried this technique but to no avail:
$$4x^2 - 5(y^2 + \frac{24}{5}y) = 16$$
$$ \Rightarrow 4x^2 - 5(y + \frac{12}{5})^2 = 16 + \left(\frac{12}{5}\right)^2$$
$$\Rightarrow 4x^2 - 5(y + \frac{12}{5})^2 = \frac{544}{25} .$$
Am I doing something wrong here? On my calculator it says that the equation should be a hyperbola

You have wrongly added $\left(\frac{12}5\right)^2$ in place of subtraction
$(2x)^2-5\{y^2-2\cdot y\cdot \frac{12}5+ (\frac{12}5)^2\}=16- \left(\frac{12}5\right)^2$
or, $(2x)^2-5\left(y- \frac{12}5\right)^2=\frac{256}{25}=\left(\frac{16}5\right)^2$
and so on
