Find an equation of the circle that has center (-6, 6) and passes through (3,-4)​

(x+6)² + (y-6)² = 181

Step-by-step explanation:

equation of the circle in general is (x - a)² + (y - b)² = r²

center is (a, b) in our task a=-6 b=6

so equation of the circle is (x+6)² + (y-6)² = r²

we have point  (3,-4)​ ⇒ x=3 y=-4

put x y in equation of the circle ⇒  (3+6)² + (-4-6)² = r² ⇒r² =181

⇒The equation of a circle is (x+6)² + (y-6)² = 181

x²+ y² - 109 = 0

Step-by-step explanation:

The coordinate of centre of circle = (-6 , 6)

Point through which it passes = (3 , -4)

So , Firstly find the distance between the centre and that point that will be equal to the radius . Using Distance Formula we have ,

⇒ D = √ [ ( x - x' )² + ( y + y')² ]

⇒ D = √ [ (3+6)² + (6+4)² ]

⇒ D = √ [ 9² + 10² ]

⇒ D = √ [ 81 + 100 ]

⇒ D = √ 181

⇒ D = 13.45 .

Now substituting the respective values in the general equation of circle .

⇒ ( x - h)² + (y - k)² = r²

⇒ { x - (-6) }² + { y - (6) }² = (13.45)²

⇒ ( x + 6 )² + ( y - 6)² = 13.45²

⇒ x² + 36 + 12x + y² + 36 -12x = 181

⇒ x² + y² + 72 = 181

⇒ x² + y² + 72 - 181 = 0

⇒ x² + y² - 109 = 0

1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!