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Chapter 10: Q 17. (page 677)

In Problem, identify the graph of each equation without completing the squares.
$2 y^{2} - x^{2} - y + x = 0$

Short Answer

Expert verified

The graph is of hyperbola.

Step by step solution

Step 1. Given information

The equation is $2 y^{2} - x^{2} - y + x = 0$ .

Step 2. Identify the graph.

Consider the equation $2 y^{2} - x^{2} - y + x = 0$ .

Compare this equation with width="194">Ax2+Cy2+Dx+Ey+F=0.

$\begin{array}{rcl} A & = & - 1 \\ C & = & 2 \\ A C & = & - 1 (2) \\ = & - 2 \\ < & 0 \end{array}$

As $A C < 0$ , the equation represents a hyperbola.

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Most popular questions from this chapter

True or False

The equation $3 x^{2} + B x y + 12 y^{2} = 10$ defines a parabola if $B = - 12$ .

To complete the square of $x^{2} - 3 x$ , add $______$ .

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

and equations are,

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

If $θ$ is acute, the Half-angle Formula for the sine function isrole="math" localid="1646654694239" $\sin \frac{θ}{2} =______$ .

Lightning Strikes Suppose that two people standing $1$ mile apart both see a flash of lightning. After a period of time, the first person standing at point $A$ hears the thunder. Two seconds later, the second person standing at point $B$ hears the thunder. If the person at point $B$ is due west of the person at point $A$ and if the lightning strike is known to occur due north of the person standing at point $A$ , where did the lightning strike occur?

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In Problem, identify the graph of each equation without completing the squares.
$2 y^{2} - x^{2} - y + x = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the graph.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In Problem, identify the graph of each equation without completing the squares.2y2-x2-y+x=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

In Problem, identify the graph of each equation without completing the squares.
$2 y^{2} - x^{2} - y + x = 0$