MCQ
Let $P \left( x _0, y _0\right)$ be the point on the hyperbola $3 x ^2-4 y ^2$ $=36$, which is nearest to the line $3 x+2 y=1$. Then $\sqrt{2}\left( y _0- x _0\right)$ is equal to :
- A$-3$
- B$9$
- ✓$-9$
- D$3$
$m =-\frac{3}{2}$
$m =+\frac{\sec \theta 3}{\sqrt{12} \cdot \tan \theta}$
$\Rightarrow \frac{3}{\sqrt{12}} \times \frac{1}{\sin \theta}=\frac{-3}{2}$
$\sin \theta=-\frac{1}{\sqrt{3}}$
$(\sqrt{12} \cdot \sec \theta, 3 \tan \theta)$
$\left(\sqrt{12} \cdot \frac{\sqrt{3}}{\sqrt{2}},-3 \times \frac{1}{\sqrt{2}}\right) \Rightarrow\left(\frac{6}{\sqrt{2}}, \frac{-3}{\sqrt{2}}\right)$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.