# 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 \(p+q\)