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Strike441 [17]
3 years ago
14

If the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle?

Mathematics
2 answers:
Varvara68 [4.7K]3 years ago
6 0
1. Find the centre of the circle or the midpoint of the two numbers
(6-6/2}, (-2+6/2)
(0, 2)
2. Find radius using the distance formula
√<span>(6 - 2)² + (-6 - 0)²
</span>√4² + (-6)²
√16 + 36
√52
r = 7.21
3. Plug in
x² + (y - 2)² = 52

So it is option D 99% sure
Mazyrski [523]3 years ago
4 0

Answer:

(D) (x-0)^2+(y-2)^2=52

Step-by-step explanation:

It is given that the endpoints of the diameter of a circle are (−6, 6) and (6, −2).

Now, the standard form equation of the circle is:

(x-a)^2+(y-b)^2=r^2

where  (a,b) are the coordinates of the center and r is  the radius.

In order to find the center, first find the midpoint of the two given points, that is:

C=(\frac{-6+6}{2}, \frac{6-2}{2})

c=(0,2)

Thus, the center is (0,2).

Now, the radius is the distance from the center to either of  the two given points, therefore using distance formula,

r^2=(-6-0)^2+(6-2)^2

r^2=52

Also, the equation of the circle is:

(x-0)^2+(y-2)^2=52

Hence, option D is correct.

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