• # question_answer The lines $y=-\frac{3}{2}x$ and $y=-\frac{2}{5}x$ intersect the curve $3{{x}^{2}}+4xy+5{{y}^{2}}-4=0$ at the points P and Q respectively. The tangents drawn to the curve at P and Q: A) intersect each other at angle of $45{}^\circ$ B) are parallel to each other C) are perpendicular to each other D) none of these

 $\frac{dy}{dx}=\frac{2y+3x}{2x+5y}$ $\Rightarrow$ ${{\left. \frac{dy}{dx} \right]}_{{{x}_{1}}{{y}_{1}}}}=0$ & ${{\left. \frac{dy}{dx} \right]}_{{{x}_{2}}{{y}_{2}}}}=\infty$$\Rightarrow$ tangents are perpendicular