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Chapter 10: Q51. (page 677)

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
$3 x^{2} - 2 x y + y^{2} + 4 x + 2 y - 1 = 0$

Short Answer

Expert verified

The equation defines ellipse.

Step by step solution

Step 1. Given Information

The given equation is $3 x^{2} - 2 x y + y^{2} + 4 x + 2 y - 1 = 0$

Here $A = 3, B = - 2, C = 1$

Step 2. Identifying Conic

$B^{2} - 4 A C = {(- 2)}^{2} - 4 (3) (1) B^{2} - 4 A C = 4 - 12 = - 8 < 0$

The equation defines ellipse.

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Most popular questions from this chapter

Whispering Gallery : Jim, standing at one focus of a whispering gallery, is $6$ feet from the nearest wall. His friend is standing at the other focus, $100$ feet away. What is the length of this whispering gallery? How high is its elliptical ceiling at the center?

If $(x, y)$ are the rectangular coordinates of a point P and $(r, θ)$ are its polar coordinate, then $x =_______$ and $y =______$ .

The graph of a parabola is given. Match graph to its equation.

$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

In Problems 19–28, find an equation for the hyperbola described. Graph the equation by hand. Center at $(0, 0)$ ; focus at $(3, 0)$ ; vertex at $(1, 0)$ .

In Problems 27–34, find two different parametric equations for each rectangular equation $y = x^{3}$

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In Problems 43–52, identify the graph of each equation without applying a rotation of axes.3x2-2xy+y2+4x+2y-1=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Identifying Conic

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Most popular questions from this chapter

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In Problems 43–52, identify the graph of each equation without applying a rotation of axes.
$3 x^{2} - 2 x y + y^{2} + 4 x + 2 y - 1 = 0$