Chapter 6: Q. 5 (page 437)

Discuss the equation $x^{2} + y^{2} - 2 x + 4 y - 4 = 0$ . Graph it.

Short Answer

Expert verified

The graph of the equation is

Step by step solution

Step 1. Given Information

We are given the equation $x^{2} + y^{2} - 2 x + 4 y - 4 = 0$ and we need to graph the equation.

Step 2. Simplifying the equation

The standard form of the equation of a circle is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

Simplifying the given equation we get:

role="math" localid="1646386481597" $\Rightarrow x^{2} + y^{2} - 2 x + 4 y - 4 = 0 \Rightarrow x^{2} - 2 x + 1 + y^{2} + 4 y + 4 = 1 + 4 + 4 \Rightarrow {(x - 1)}^{2} + {(y + 2)}^{2} = 9 \Rightarrow {(x - 1)}^{2} + {(y + 2)}^{2} = {(3)}^{2}$

Comparing the equation with the standard form we get the center of the circle is at $(1, - 2)$ and radius is $3$ units.

Step 3. Plotting the graph

The graph of the equation is:

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Discuss the equation $x^{2} + y^{2} - 2 x + 4 y - 4 = 0$ . Graph it.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the equation

Step 3. Plotting the graph

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Discuss the equation x2+y2-2x+4y-4=0. Graph it.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the equation

Step 3. Plotting the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Pure Maths

Logic and Functions

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Discuss the equation $x^{2} + y^{2} - 2 x + 4 y - 4 = 0$ . Graph it.