Answer:
Center: ( -1 , 2 )
Radius: 6
Step-by-step explanation:
The equation for a circle is given as follow:
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
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:
[tex](x+1)^{2} +(y-2)^{2} =36[/tex]
the Center is: (-1,2)
and the radius is: [tex]\sqrt{36}[/tex] = 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:
[tex](x+1)^{2} +(y-2)^{2} =36[/tex]
[tex](x+1)^{2} +(2-2)^{2} =36[/tex]
[tex](x+1)^{2} +(0)^{2} =36[/tex]
[tex](x+1)^{2} =36[/tex]
[tex]x+1 =±\sqrt{36}[/tex]
[tex]x=6-1[/tex] AND [tex]x=-6-1[/tex]
[tex]x=5[/tex] AND [tex]x=-7[/tex]
- The points are A(5,2) and B(-7,2)
second sub x= -1 in the equation to find the values for y:
[tex](x+1)^{2} +(y-2)^{2} =36[/tex]
[tex](-1+1)^{2} +(y-2)^{2} =36[/tex]
[tex](0)^{2} +(y-2)^{2} =36[/tex]
[tex](y-2)^{2} =36[/tex]
[tex]y-2=±\sqrt{36}[/tex]
[tex]y=6+2[/tex] AND [tex]y=-6+2[/tex]
[tex]y=8[/tex] AND [tex]y=-4[/tex]
- 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:
