Question

If the line y=mx+1 touches the hyperbola $\frac{x^z}{9}-\frac{y^z}{2}$ = 1 then m =

• A. ± $\frac{1}{3}$
• B. ± $\frac{1}{\sqrt{2}}$
• C. ± $\frac{1}{2}$
• D. ± $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D

± $\frac{1}{\sqrt{3}}$

Y = mx + 1 $\frac{x^z}{9}-\frac{y^z}{2}$ = 1

1 = 9$m^2$ - 2 $\Rightarrow$ $9m^2$ = 3 $\Rightarrow$ $m^2$ = $\frac{1}{3}$ $\Rightarrow$ m = ± $\frac{1}{\sqrt{3}}$