Question

Tangent are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1$. The points of contact of the tangents on the hyperbola are

• A. $(\frac{9}{2\sqrt{2}},\frac{1}{\sqrt{2}})$
• B. $(-\frac{9}{2\sqrt{2}},-\frac{1}{\sqrt{2}})$
• C. $(3\sqrt{3},-2\sqrt{2})$
• D. $(-3\sqrt{3},2\sqrt{2})$

Answer 1

Answer: (A), (B)

$(-\frac{9}{2\sqrt{2}},-\frac{1}{\sqrt{2}})$

hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$

Slope of tangent $=2$

Equation of tangents
$y=2x+c$
$y=2x\pm \sqrt{a^2{m}^2-b^2}$

$\Rightarrow y=2x\pm \sqrt{32}$
$\Rightarrow y=2x\pm 4\sqrt{2}$
Points of contact $=(\frac{\pm a^{2}m}{c},\pm \frac{b^2}{c})$

$\therefore (\pm \frac{9}{2\sqrt{2}},\pm \frac{1}{\sqrt{2}})$