Question

Equation of tangent to the hyperbola $ 2{{x}^{2}}-3{{y}^{2}}=6 $ which is parallel to the line $ y=3x+4, $ is

• A. $ y=3x-4 $
• B. $ y=3x-5 $
• C. $ y=3x+5 $
• D. $ y=3x\pm 5 $

Answer 1

Answer: (D)

Given hyperbola is
$ 2{{x}^{2}}-3{{y}^{2}}=6 $
$ \Rightarrow $ $ \frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1 $
Here, $ {{a}^{2}}=3,\text{ }{{b}^{2}}=2 $
Since, tangent is parallel to $ y=3x+4 $
$ \therefore $ Here, $ m=3 $
Thus, tangent of hyperbola is
$ y=mx\pm \sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}} $
$ \Rightarrow $ $ y=3x\pm \sqrt{3.9-2} $
$ \Rightarrow $ $ y=3x\pm 5 $