Find the center and radius of a circle with the equation x² + y2 +6x

Determine the equation of the circle graphed below. ( please help me )

Brums [2.3K]

Answer:

$Equation : \\(x+3)^2 + ( y -2)^2 = 36$

Step-by-step explanation:

For standard form the circle's equation we need the centre of the circle and the radius.

Step 1: Find the centre

If the centre is not given find the end points of the diameter

and then find the mid point.

Let the end points of the diameter be : ( - 3 , 8 ) and ( -3 , -4 )

The mid-point of the diameter is :

$Mid-point = (\frac{-3 + - 3}{2}, \frac{-4+8}{2}) = (-3, 2)$

Therefore, centre of the circle = ( -3 , 2 )

Step 2 : Find radius

$Radius = \frac{Diameter }{2}$

Diameter is the distance between the end points ( -3 , 8) and ( -3 , -4 )

That is ,

$Diameter = \sqrt{(-3-(-3))^2 + ( -4 -8)^2}\\$

$= \sqrt{(-3 + 3)^2 + (-12)^2}\\\\=\sqrt{0 + 144}\\\\=12$

Therefore ,

$Radius = \frac{12}{2} = 6$

Step 3 : Equation of the circle

Standard equation of the circle with centre ( h ,k )

and radius ,r is :

$(x - h)^2+(y -k)^2 = r^2$

Therefore, the equation of the circle with centre ( -3, 2)

and radius = 6 is :

$(x - (-3))^2 + (y - 2)^2 = 6^2\\\\(x + 3)^2 + (y - 2)^2 = 36$

5 0

2 years ago

What is the area of the triangle? no links just the answer plz.

nikitadnepr [17]

Answer:

A = 25

Step-by-step explanation:

Base = |-2-(-7)| = |-2+7| = 5

equation of the line that includes the base

x = 6 (because it is parallel to y axis)

the height passes to the point (-4,-4) and must be perpendicular to the base

the equation of the line of the base hasn’t the slope expressed, so the line of the height has a slope equal to 0

so the equation of the line is y= -4

the point (6,-4) is where the two lines intercept and it is the point where the height hit the base

height = |-4-6| = 10

A = (base x height)/2 = (5x10)/2 = 25

3 0

2 years ago

A quilt is designed using a square pattern. each square contains two rectangles. each rectangle contains a shaded rhombus. each

Xelga [282]

Based on the calculations, the value of x in this rhombus is equal to: B. 55.

<h3>How to determine the value of x?</h3>

Since the opposite angles in a rhombus are always congruent, the sum of each angle in any rhombus must be equal to 360 degrees.

From the image of the rhombus, we can deduce the following parameters:

Adjacent angles = 2x + 20 and 50 degrees.

Opposite angles = 2x + 20 and 50 degrees.

Adding the angles, we have:

2x + 20 + 2x + 20 + 50 + 50 = 360

4x + 140 = 360

4x = 360 - 140

4x = 220

x = 220/4

x = 55°

Read more on rhombus here: brainly.com/question/11586845

#SPJ4

8 0

1 year ago

PLS I NEED HELP PLSS!!!!

Sergio039 [100]

Answer:

the answer is.........................................E

5 0

2 years ago

I need help with #10 please! Thanks!

Anastasy [175]

√27 can be simplified. First we split it into √9√3 because 9*3=27. Now the √9 becomes 3. We can multiply this 3 with the 3 in the beginning of the problem to get 9√3 as the final answer

Hope this helps

7 0

3 years ago

Find the center and radius of a circle with the equation x² + y2 +6x–8y +16= 0.