Maharashtra Board Solutions for Chapter: Conic Sections, Exercise 3: EXERCISE 7.3

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 $9{\mathrm{x}}^2-16{\mathrm{y}}^2=144$ at the point L of latus rectum in the first quadrant.

Show that the line $3\mathrm{x}–4\mathrm{y}+10=0$is tangent to the hyperbola${\mathrm{x}}^2–4{\mathrm{y}}^2=20$. Also find the point of contact.

If the line $3\mathrm{x}–4\mathrm{y}=\mathrm{k}$touches the hyperbola  $\frac{{\mathrm{x}}^2}{5}-\frac{4{\mathrm{y}}^2}{5}=1$ then find the value of $\mathrm{k}$. 

Find the equations of the tangents to the hyperbola $\frac{{\mathrm{x}}^2}{25}-\frac{{\mathrm{y}}^2}{9}=1$ making equal intercepts on the co-ordinate axes.

Find the equations of the tangents to the hyperbola $5{\mathrm{x}}^2-4{\mathrm{y}}^2=20$ which are parallel to the line $3\mathrm{x}+2\mathrm{y}+12=0$.