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Kobotan [32]
2 years ago
15

Determine the equation of the circle graphed below. ( please help me )

Mathematics
1 answer:
Brums [2.3K]2 years ago
5 0

Answer:

Equation : \\(x+3)^2 + ( y -2)^2 = 36

Step-by-step explanation:

For standard form the circle's equation we need the centre of the circle and the radius.

Step 1: <em><u>Find the centre</u></em>

If the centre is not given find the end points of the diameter

and then find the mid point.

Let the end points of the diameter be : ( - 3 , 8 ) and ( -3 , -4 )

The mid-point of the diameter is :

                        Mid-point = (\frac{-3 + - 3}{2}, \frac{-4+8}{2}) =  (-3, 2)

Therefore, centre of the circle = ( -3 , 2 )

Step 2 : <u>Find radius</u>

<u></u>Radius = \frac{Diameter }{2}<u></u>

Diameter is the distance between the end points ( -3 , 8) and ( -3 , -4 )

That is ,

 Diameter = \sqrt{(-3-(-3))^2 + ( -4 -8)^2}\\

                 = \sqrt{(-3 + 3)^2 + (-12)^2}\\\\=\sqrt{0 + 144}\\\\=12

Therefore ,

       Radius = \frac{12}{2} = 6

Step 3 : <u>Equation of the circle</u>

Standard equation of the circle with centre ( h ,k )

and radius ,r is :

       (x - h)^2+(y -k)^2 = r^2

Therefore, the equation of the circle with centre ( -3, 2)

and radius = 6 is :

    (x - (-3))^2 +  (y - 2)^2 = 6^2\\\\(x + 3)^2 + (y - 2)^2 = 36

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