(x - 2)2 + (y + 3)2 = 4
=

Question

12-05-2022
Mathematics

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(x - 2)2 + (y + 3)2 = 4
=

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worthenkamari worthenkamari · Answer 1 · 2022-05-12T04:27:49+02:00

Answer:

Step-by-step explanation:Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(x-2)*2+(y+3)*2-(4)=0

STEP

1

:

Equation at the end of step 1

(((x - 2) • 2) + 2 • (y + 3)) - 4 = 0

STEP

2

:

Equation at the end of step 2

(2 • (x - 2) + 2 • (y + 3)) - 4 = 0

STEP

3

:

STEP

4

:

Pulling out like terms :

4.1 Pull out like factors :

2x + 2y - 2 = 2 • (x + y - 1)

Equation at the end of step

4

:

2 • (x + y - 1) = 0

STEP

5

:

Equations which are never true:

5.1 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

5.2 Solve x+y-1 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line x+y-1 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.00000

y-intercept = 1/1 = 1.00000

Calculate the X-Intercept :

When y = 0 the value of x is 1/1 Our line therefore "cuts" the x axis at x= 1.00000

x-intercept = 1/1 = 1.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.000 and for x=2.000, the value of y is -1.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.000 - 1.000 = -2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -2.000/2.000 = -1.000

Geometric figure: Straight Line

Slope = -2.000/2.000 = -1.000

x-intercept = 1/1 = 1.00000

y-intercept = 1/1 = 1.00000

(x - 2)2 + (y + 3)2 = 4 =

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(x - 2)2 + (y + 3)2 = 4
=