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Chapter 10: Q46. (page 677)

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

Short Answer

Expert verified

The equation defines ellipse.

Step by step solution

01

Step 1. Given Information

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

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

02

Step 2. Identifying Conic

$B^{2} - 4 A C = {(- 3)}^{2} - 4 (2) (2) B^{2} - 4 A C = 9 - 16 = - 7 < 0$

The equation defines ellipse.

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Most popular questions from this chapter

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

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

Semi elliptical Arch Bridge: A bridge is built in the shape of a semi elliptical arch. The bridge has a span of $120$ feet and a

maximum height of $25$ feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances

of $10, 30$ and $50$ feet from the center.

In Problems 43–52, identify the graph of each equation without applying a rotation of axes. $x^{2} + 3 x y - 2 y^{2} + 3 x + 2 y + 5 = 0$

Graph each function.

$f (x) = - \sqrt{4 - 4 x^{2}}$

Prove that the hyperbola

$\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1$

has the two oblique asymptotes $y = \frac{a}{b} x$ and $y = - \frac{a}{b} x$

See all solutions

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