hyperbola: equation for tangent lines and normal lines

Question

Find the equations for (a) the tangent lines, and (b) the normal lines, to the hyperbola $y^2/4 - x^2/2 = 1$ when $x = 4$.

Answer 1

If $x=4, \frac{y^2}4=1+\frac{4^2}2=9\implies y=\pm6$

Using Article 305 of this, the tangent of $$\frac{y^2}4-\frac{x^2}2=1$$ at $(h,k)$ is $$ \frac{y\cdot k}4-\frac{x\cdot h}2=1$$

Do you know how to find the perpendicular of a given line from a given point $(4,\pm 6)$?