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Chapter 10: Q 18. (page 677)

In Problem, identify the graph of each equation without completing the squares.
$y^{2} - 8 x^{2} - 2 x - y = 0$

Short Answer

Expert verified

The graph is of hyperbola.

Step by step solution

01

Step 1. Given information

The equation is $y^{2} - 8 x^{2} - 2 x - y = 0$ .

02

Step 2. Identify the graph.

Consider the equation $y^{2} - 8 x^{2} - 2 x - y = 0$ .

Compare this equation with $A x^{2} + C y^{2} + D x + E y + F = 0$ .

$\begin{array}{rcl} A & = & - 8 \\ C & = & 1 \\ A C & = & - 8 \\ < & 0 \end{array}$

So, the equation represents a hyperbola.

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Most popular questions from this chapter

Find the intercepts of the equation $y^{2} = 16 - 4 x^{2}$ .

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