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Dominik [7]
3 years ago
11

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

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
8 0

Answer:

Center: ( -1 , 2 )

Radius: 6

Step-by-step 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: \sqrt{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 =±\sqrt{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=±\sqrt{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:

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