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soldi70 [24.7K]
3 years ago
8

Hello! I need help on this. Thanks! :)

Mathematics
1 answer:
Valentin [98]3 years ago
6 0
(1,0) and (6,2) are not on the same line and I don't understand the last question
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The endpoints of the diameter of a circle are (−2, −3) and (4, −1). Which equation represents the circle?
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Answer:

The equation of circle is (x-1)^{2}+(y-2)^{2} = 18

Step-by-step explanation:

Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)

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

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

(  \frac{x1+x2}{2} , \frac{y1+y2}{2}  )

( \frac{-2+4}{2} , \frac{-3-1}{2}  )

(1,2)

Hence (h,k) is (1,2)

Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get

(4-1)^{2} +(-1-2)^{2} = r^{2}

r^{2} = 18

Now substituting values of (h,k) and r^{2} in equation of circle, we get

(x-1)^{2}+(y-2)^{2} = 18

Hence the equation of circle is (x-1)^{2}+(y-2)^{2} = 18

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