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Chapter 10: Q 14. (page 677)

In Problem, identify the graph of each equation without completing the squares.

2x2+y2-8x+4y+2=0

Short Answer

Expert verified

An equation represents a graph of an ellipse.

Step by step solution

01

Step 1. Given information

An equation is2x2+y2-8x+4y+2=0.

02

Step 2. Identify the graph.

The conic is given by the equation given below.

2x2+y2-8x+4y+2=0

The conic can be determined calculating the value of B2-4AC.

B2-4AC=(0)2-4(2)(1)=-8

The value of B2-4ACis negative and therefore the given conic is an ellipse since Ais not equal toB.

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Most popular questions from this chapter

A hyperbola for which a=bis called an equilateral hyperbola. Find the eccentricity eof an equilateral hyperbola.

[Note: The eccentricity of a hyperbola is defined in Problem 81.]

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

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

The point that is symmetric with respect to the y-axis to the point (-2,5)is _____.

Prove that the hyperbola

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has the two oblique asymptotesy=abxandy=-abx

Find an equation for each ellipse. Graph the equation by hand.

Center at (1,2): focus at(1,4): contains the point(2,2)
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