Find the equation of the hyperbola referred to its principal axes whose distance between directrices is $\frac{8}{3}$ and eccentricity is $\frac{3}{2}.$

Find the equation of the hyperbola referred to its principal axes whose length of conjugate axis $=12$ and passing through$(1,-2)$.

 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 $(4,3)$.