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Chapter 10: Q.22 (page 699)

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

4x2+10xy+4y2-9=0

Short Answer

Expert verified

The conic represented by the given equation is a hyperbola.

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.

4x2+10xy+4y2-9=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=4,B=10,C=4

Plugging the values:

B2-4AC=102-444=100-64=36

Since B2-4AC>0, the given conic is a hyperbola.

03

Step 3. Conclusion

Hence, the conic represented by the given equation is a hyperbola.

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Most popular questions from this chapter

True or False

The equation 3x2+Bxy+12y2=10defines a parabola ifB=-12.

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

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

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

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

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

Ax24-y2=1Bx2-y24=1Cy24-x2=1Dy2-x24=1

Graph:

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.x2+3xy-2y2+3x+2y+5=0
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