Question

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:

Answer 1

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: