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2. Given the equation of a circle in standard form, identify the center, radius, and graph the circle.

(x + 1)2 + (y - 2)2 = 36

Center:
Radius:

2. Given the equation of a circle in standard form, identify the center, radius, and-example-1

1 Answer

5 votes

Answer:

Center: ( -1 , 2 )

Radius: 6

Explanation:

The equation for a circle is given as follow:


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

Where,

the Center is: ( h , k ) (note that the signs of the number are different)

and the radius is: r

So if we compare the original circle equation to the equation in the question we can see that:


(x+1)^(2) +(y-2)^(2) =36

the Center is: (-1,2)

and the radius is:
√(36) = 6

2. To draw the graph find points that lay on the circle, it's better to take the values of x and y from the Center:

first sub y=2 in the equation to find the values for x:


(x+1)^(2) +(y-2)^(2) =36


(x+1)^(2) +(2-2)^(2) =36


(x+1)^(2) +(0)^(2) =36


(x+1)^(2) =36


x+1 =±√(36)


x=6-1 AND
x=-6-1


x=5 AND
x=-7

  • The points are A(5,2) and B(-7,2)

second sub x= -1 in the equation to find the values for y:


(x+1)^(2) +(y-2)^(2) =36


(-1+1)^(2) +(y-2)^(2) =36


(0)^(2) +(y-2)^(2) =36


(y-2)^(2) =36


y-2=±√(36)


y=6+2 AND
y=-6+2


y=8 AND
y=-4

  • The points are D(-1,8) and E(-1,-4)

After finding the points write them in the graph and match them together to get the like the circle in the picture below:

2. Given the equation of a circle in standard form, identify the center, radius, and-example-1
User Ben McNiel
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