The Ellipsoid

The equation to the tangent plane to the ellipsoid $x^2+4y^2+9z^2=1$ at point $(\frac{1}{2},\frac{1}{4},\frac{\sqrt(2)}{3})$ can be represented as $a(x-\frac{1}{2})+b(y-\frac{1}{4})+(z-\frac{\sqrt 2}{3}$ =o

$ab$ can be written as $\frac{p}{q}$ where $p$ and $q$ are perfect squares. Find $p+q$