Q. 67 In Problems 65-70, graph each eq... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 11: Q. 67 (page 773)

In Problems $65 - 70$ , graph each equation and find the point(s) of intersection, if any.
The circle ${(x - 1)}^{2} + {(y + 2)}^{2} = 4$ and the parabola $y^{2} + 4 y - x + 1 = 0$ .

Short Answer

Expert verified

The graph of the parabola $y^{2} + 4 y - x + 1 = 0$ and the circle ${(x - 1)}^{2} + {(y + 2)}^{2} = 4$ is,

From the graph, the two equations are intersecting at two points They are, $(0, - \sqrt{3} - 2), (1, 0), (0, \sqrt{3} - 2), (1, - 4)$ .

Step by step solution

Step 1. Given information

$y^{2} + 4 y - x + 1 = 0 {(x - 1)}^{2} + {(y + 2)}^{2} = 4$

First solve each equation for $y$ .

Consider the first equation,

$y^{2} + 4 y - x + 1 = 0 y^{2} + 4 y = x - 1 y^{2} + 4 y + 4 = x - 1 + 4 {(y + 2)}^{2} = x + 3 y + 2 = 卤 \sqrt{x + 3} y = 卤 \sqrt{x + 3} - 2$

Next consider the second equation,

${(x - 1)}^{2} + {(y + 2)}^{2} = 4 {(y + 2)}^{2} = 4 - {(x - 1)}^{2} y + 2 = 卤 \sqrt{4 - {(x - 1)}^{2}} y = 卤 \sqrt{4 - {(x - 1)}^{2}} - 2$

Step 2. Now sketch a graph by using the obtained equations.

From the graph, the two equations are intersecting at two points. They are, $(0, - \sqrt{3} - 2), (1, 0), (0, \sqrt{3} - 2), (1, - 4)$ .

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91影视

In Problems $65 - 70$ , graph each equation and find the point(s) of intersection, if any.
The circle ${(x - 1)}^{2} + {(y + 2)}^{2} = 4$ and the parabola $y^{2} + 4 y - x + 1 = 0$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Now sketch a graph by using the obtained equations.

One App. One Place for Learning.

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91影视

In Problems 65-70, graph each equation and find the point(s) of intersection, if any.The circlex-12+y+22=4and the parabolay2+4y-x+1=0.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Now sketch a graph by using the obtained equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In Problems $65 - 70$ , graph each equation and find the point(s) of intersection, if any.
The circle ${(x - 1)}^{2} + {(y + 2)}^{2} = 4$ and the parabola $y^{2} + 4 y - x + 1 = 0$ .