Identify the type of conic represented by $2x^2-4xy+5y^2-6x+8y-7=0$.

Step-by-step solution

1. Extract $A$, $B$, and $C$ from the general quadratic $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$: $A=2$, $B=-4$, $C=5$.
2. Compute the discriminant $B^2-4AC$: $(-4{)}^2-4(2)(5)=16-40=-24$.
3. Since the discriminant is negative, the conic is an ellipse or a circle.\nCheck if $A=C$ for a circle; here $2eq5$, so it is an ellipse.\nThus the conic is an ellipse.

Concept tested: Classification using discriminant

Published 13 October 2026 · How this solution was prepared and checked