Find the equation of the hyperbola referred to its principal axes which passes through the points $(6,9)$ and $(3,0).$

 Find the equation of the hyperbola referred to its principal axes whose vertices are $(\pm 7,0)$and end points of conjugate axis are $(0,\pm 3)$.

Find the equation of the hyperbola referred to its principal axes whose foci are at$(\pm 2,0)$and eccentricity $\frac{3}{2}$.

Find the equation of the hyperbola referred to its principal axes whose length of transverse and conjugate axis are $6$ and $9$ respectively. 

Find the equation of the hyperbola referred to its principal axes whose length of transverse axis is $8$ and distance between foci is $10.$

Find the equation of the tangent to the hyperbola $3{\mathrm{x}}^2-{\mathrm{y}}^2=4$ at the point $(2,2\sqrt{2})$

Find the equation of the tangent to the hyperbola $3x^2-y^2=12$ at the point $(4,3)$.

Find the equation of the tangent to the hyperbola $\frac{{\mathrm{x}}^2}{144}-\frac{{\mathrm{y}}^2}{25}=1$ at the point whose eccentric angle is $\frac{\mathrm{\pi }}{3}$

Find the equation of the tangent to the hyperbola $\frac{{\mathrm{x}}^2}{16}-\frac{{\mathrm{y}}^2}{9}=1$ at the point in a first quadrant whose ordinate is $3$.