Using the following equation, find the center and radius of the circle. you must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20 explain

The center (C) and radius (r) of the circle from equation   x² + 2x + y² + 4y = 20 is  C = ((-1,-2) and r = 5

Circles are a flat object that has dots equal distance to the center of the circle

This distance is called the radius

Circle general equation

The general form of the quadratic equation of a circle is

x² + y² + Ax + By + C = 0

where the center of the circle is:

(A, B) =

while for the radius of the circle is

The known circle equation in the question is

x² + 2x + y² + 4y = 20

We change to the common circle circle to be:

x² + 2x + y² + 4y-20 = 0

Then from this equation the values ​​of A, B and C are:

A = 2

B = 4

and C = -20

So that

The center (C)

(

C = ((-1,-2)

While radius (r)

r =

r = √25

r = 5

derive the equation of a circle

the standard equation of each circle

the circle of the center and radius are given

the standard equation for a circle centered at the origin

Center : (-1,-2)

Radius : 5

Step-by-step explanation:

The equation for the circle is given by

Comparing, the equation with

2g = 2 => g = 1

2f = 4 => f = 2

c = -20

Now, the center of the circle = (-g,-f) = (-1, -2)

Center of the circle is given by

Therefore, the radius of the circle is 5.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: