Answer in Analytic Geometry for RAKESH DEY #86620

Question #86620

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

Expert's answer

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.

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Comments

Assignment Expert

03.09.19, 16:59

The conic also may be traced with a help of a special software (see https://www.math.fsu.edu/~bellenot/class/s10/cla/other/qform.pdf).

Assignment Expert

03.09.19, 16:59

There are different ways to find the canonical equation in a new coordinate system. For example, using eigenvalues (hints can be found at https://www.sangakoo.com/en/unit/reduced-and-canonical-equations-of-the-conics) or using a substitution x=Xcos(t)-Ysin(t),, y=Xsin(t)+Ycos(t) (hints can be found at Example 3, https://www.cengage.com/resource_uploads/downloads/1285060288_382318.pdf).

Dharmendra Kumar

03.09.19, 00:31

here is just identification ..where is tracing steps