Mathematics - Matrices Question with Solution | TestHub

$$\begin{array}{rl}& x^2-6y\\ & 2x^2-4y^2=9\end{array}$$ Consider the line, $$x-y=\frac{3}{2}$$ On solving (i) and (iii), we get only $$x=3,y=\frac{3}{2}$$ Hence $\left(3,\frac{3}{2}\right)$ is the point of contact of conic (i), and line (iii) On solving (ii) and (iii), we get only $x=3$, $$y=\frac{3}{2}$$ Hence $\left(3,\frac{3}{2}\right)$ is also the point of contact of conic (ii) and line (iii). Hence line (iii) is the common tangent to both the given conics.