Question

The line $y=mx+2$ touches the hyperbola $4x^2-9y^2=36$ then $m=$

• A. $\pm \frac{2}{3}$
• B. $\pm \frac{2\sqrt{2}}{3}$
• C. $\pm \frac{9}{8}$
• D. $\pm \frac{4\sqrt{2}}{3}$

Answer 1

The correct option is B $\pm \frac{2\sqrt{2}}{3}$

Given that,

$4x^2-9y^2=36$

$\frac{x^2}{9}-\frac{y^2}{4}=1$ …… (1)

Since, the line $y=mx+2$ touches to this hyperbola.

We know that the condition a line touches to hyperbola

$c^2=a^2{m}^2-b^2$

Therefore,

$2^2=9m^2-4$

$9m^2=4+4$

$m^2=\frac{8}{9}$

$m=\pm \frac{2\sqrt{2}}{3}$

Hence, this is the answer.