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Chapter 10: Q 19. (page 677)

In Problem, identify the graph of each equation without completing the squares.
$x^{2} + y^{2} - 8 x + 4 y = 0$

Short Answer

Expert verified

The graph is of a circle.

Step by step solution

01

Step 1. Given information

The equation is $x^{2} + y^{2} - 8 x + 4 y = 0$ .

02

Step 2. Identify the graph.

Consider the equation $x^{2} + y^{2} - 8 x + 4 y = 0$ .

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

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

So, the equation represents a circle.

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Most popular questions from this chapter

In Problem, identify the graph of each equation without completing the squares.

$6 x^{2} + 3 y^{2} - 12 x + 6 y = 0$

Find an equation for each ellipse. Graph the equation by hand.

Vertices at $(2, 5)$ and $(2, - 1)$ :c=2

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,

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

Find an equation for each ellipse. Graph the equation by hand.

Center at $(1, 2)$ : focus at $(4, 2)$ : contains the point $(1, 3)$

See all solutions

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