Discussion Forum

The distance between the tangents to the hyperbola  $\frac{x^{2}}{20}- \frac{3y^{2}}{4}$=1 which are parallel to the line x+3y=7 is 

Answer:

Explanation:

 Equation  of tangent to hyperbola  $\frac{x^{2}}{20}- \frac{3y^{2}}{4}$=1

parallel to x+3y=7 is

 $y=-\frac{1}{3}x\pm\sqrt{\frac{20}{9}-\frac{4}{3}}$

$3y=-x\pm2\sqrt{2}$

 $x+3y=2\sqrt{2}$

and  $x+3y=-2\sqrt{2}$

Distance between parallel tangent is 

$d=\frac{2\sqrt{2}+2\sqrt{2}}{\sqrt{1+3^{2}}}=\frac{4\sqrt{2}}{\sqrt{10}}=\frac{4}{\sqrt{5}}$