Question

Equation of tangent to the hyperbola \[2x^{2}-3y^{2}=6\] which is parallel to the line y = 3x + 4, is______.

Options

• \[y=3x+5\]

• \[y=3x-5\]

• \[y=3x+5\] and \[y=3x-5\]

• None of these

Answer 1

Equation of tangent to the hyperbola \[2x^{2}-3y^{2}=6\] which is parallel to the line y = 3x + 4, is \[y=3x+5\] and \[y=3x-5\].

Explanation:

Here, \[a^{2}=3,b^{2}=2,m=3\] and the equation of tangent to hyperbola is 

\[y=mx\pm\sqrt{(a^2m^2-b^2)}\]

\[\Rightarrow\quad y=3x\pm5\]