Question

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

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

Answer 1

Answer: (A), (C)

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

As, points of contact
$=(\frac{\pm a^{2}m}{\sqrt{a^2{m}^2-b^2}},\frac{\pm b^2}{\sqrt{a^2{m}^2-b^2}})$
Here, $a^2=9,b^2=4,m=2$
So, required points are $(\frac{\pm 9}{2\sqrt{2}},\frac{\pm 1}{\sqrt{2}})$