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Chapter 10: Q.23 (page 699)

In Problems 19 鈥�23, identify each conic without completing the squares and without applying a rotation of axes.

x2-2xy+3y2+2x+4y-1=0

Short Answer

Expert verified

The conic represented by the given equation is an ellipse.

Step by step solution

01

Step 1. Given Information

Given to identify the conic without completing the squares and without applying a rotation of axes.

x2-2xy+3y2+2x+4y-1=0

02

Step 2. Calculation

An equation of the form Ax2+Bxy+Cy2+Dx+Ey+F=0defines:

  • a parabola if B2-4AC=0
  • an ellipse/ a circle if B2-4AC<0
  • a hyperbola if B2-4AC>0

In the given equation, A=1,B=-2,C=3

Plugging the values,

B2-4AC=-22-413=4-12=-8

Since B2-4AC<0, the given conic is an ellipse or a circle.

SinceA鈮�C, the conic is an ellipse.

03

Step 3. Conclusion

Hence, the conic represented by the given equation is an ellipse.

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