I have a specific conic (which I've worked out is a parabola)
$16x^2 - 24xy + 9y^2 - 60x - 80y + 20 = 0$
I have to use a rotation through an angle $\theta$ where $sin\theta=4/5$ and $cos\theta = -3/5$ and then a translation.
I have done roughly 3 pages trying to work this out, but I'm just questioning whether I am approaching it the right way.
I have used the equations $x=x'cos\theta - y'sin\theta$ and $y=x'sin\theta + y'cos\theta$. So just plugged in my cos and sin and substituted these into my original equation.
This doesn't come out as a nice looking equation and I'm sure it's wrong so is there an easier way to do this?
I got $\frac{432}{25}x^2 + \frac{864}{25}xy - \frac{32}{25}y^2 - \frac{104}{5}x + \frac{453}{5}y + 20 = 0$.
If anyone could point me in the right direction I'd be highly appreciative.