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sveticcg [70]
3 years ago
7

The equation of circle having a diameter with endpoints (-2, 1) and (6, 7) is

Mathematics
1 answer:
densk [106]3 years ago
8 0

Answer:

(x-2)^{2}+(y-4)^{2}=25

Step-by-step explanation:

step 1

Find the diameter of the circle

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

A(-2,1)\\B(6,7)  

substitute the values

d=\sqrt{(7-1)^{2}+(6+2)^{2}}

d=\sqrt{(6)^{2}+(8)^{2}}

d=\sqrt{100}

d=10\ units

The radius is half the diameter

so

r=10/2=5\ units

step 2

Find the center of the circle

the center of the circle is the midpoint between the endpoints of the diameter

so

The center is

(\frac{-2+6}{2},\frac{1+7}{2})

(2,4)

step 3

Find the equation of the circle

The equation of the circle is

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

substitute the values

(x-2)^{2}+(y-4)^{2}=5^{2}

(x-2)^{2}+(y-4)^{2}=25

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