I know how to change a rectangular equation into a parametric one but can't do it vice versa.
An example is: (x+2)^2/25-(y-5)^2/12=1
I'm flabbergasted!
Hello cheet0faceThere are no hard and fast rules about doing it this way round, but the equation you mention is a fairly standard one - it's a hyperbola, and a variation on the simpler version:
$\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2}=1$
except that its centre has been moved from the origin to $\displaystyle (-2, 5)$.
We use trig functions to write equations like this in parametric form. In this case we can use the fact that $\displaystyle \sec^2\theta - \tan^2\theta= 1$, by writing:
$\displaystyle x=5\sec \theta - 2$ and $\displaystyle y = 2\sqrt3\tan\theta + 5$
You'll see that if you eliminate $\displaystyle \theta$ between these two equations you get:
$\displaystyle \frac{x+2}{5} = \sec\theta$ and $\displaystyle \frac{y-5}{2\sqrt3}=\tan\theta$
So, using the above trig identity:
$\displaystyle \frac{(x+2)^2}{25} - \frac{(y-5)^2}{12} = 1$
Grandad