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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

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?

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 $(1, 0)$ .

To graph $y = {(x - 3)}^{2} + 1$ , shift the graph of $y = x^{2}$ to the right________ units and then________ 1 unit.

Except for degenerate cases, the equation $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ defines $a (n)__________$ if $B^{2} - 4 A C = 0$ .

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at $(4, 0)$ and vertex at $(0, 0)$ .

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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.

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Most popular questions from this chapter

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