Answer to Question #86620 in Analytic Geometry for RAKESH DEY

Question

identify and trace the conic x2-2xy+y2-3x+2y+3=0

Answer 1

Please refer to link:

https://en.wikipedia.org/wiki/Conic_section#General_Cartesian_form

General Cartesian form of the equation is:

$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0; \\$

If discriminant is equal to zero, the equation represents a parabola.

$B^2 - 4AC = 2^2 - 4\times1\times1 = 0. \\$

Therefore it is a parabola.

Figure: parabola.