Thank you for reporting, we will resolve it shortly
Q.
Equation of the tangent to the hyperbola $ 2{{x}^{2}}-3{{y}^{2}}=6 $ . Which is parallel to the line $ y-3x-4=0 $ is
Jharkhand CECEJharkhand CECE 2009
Solution:
Let the equation of a line which is parallel to the line
$ y-3x-4=0 $ is $ y=3x+k $
Since, this is tangent to the hyperbola
$ \frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1 $
$ \therefore $ $ k=\sqrt{3{{(3)}^{2}}-2} $
$ (\because \,\,k=\sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}}) $
$ =\sqrt{25}=5 $
$ \therefore $ Required line is $ y=3x+5 $ ,