(c) Given equation is $(x - 1)^{2} + (y - 2)^{2} = 3 \times \left( \ \ \ \frac{2x + 3y - 2}{\sqrt{13}} \right)^{2}$ On comparing with $PS = ePM$ $\therefore\ e = 3$ Hence, it represents a hyperbola
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.