Chapter 13 - Conic Sections - 13.3 Conic Sections: Hyperbolas - 13.3 Exercise Set - Page 871: 41

Circle

$3{{x}^{2}}+{{y}^{2}}-x=2{{x}^{2}}-9x+10y+40$ Combine like terms $3{{x}^{2}}-2{{x}^{2}}+{{y}^{2}}-x+9x-10y-40=0$ ${{x}^{2}}+{{y}^{2}}+8x-10y-40=0$ Compare the equation ${{x}^{2}}+{{y}^{2}}+8x-10y-40=0$ with the standard equation of a conic section $A{{x}^{2}}+B{{y}^{2}}+Cxy+Dx+Ey+F=0$, Here, $A=1,B=1$ (A = B) Therefore, the graph of the equation is a circle.