Verified answer

Ola Luisa

C(0,k)

x² + (y - k)² = r²

3² + (4 - k)² = r²

1² + (6 - k)² = r²

x² + y² - 2ky + k² = r²

9 + 16 - 8k + k² = r²

1 + 36 - 12k + k² = r²

x² + y² - 2ky = r² - k²

25 - 8k = r² - k²

37 - 12k = r² - k²

25 - 8k = 37 - 12k

12k - 8k = 37 - 25

4k = 12

k = 3

x² + (y - 3)² = r²

3² + (4 - 3)² = r²

9 + 1 = r²

r² = 10

equação

x² + (y - 3)² = 10

pronto

C(0, y)..........C(0, y)

A(3, 4)..........B(1, 6)

(0-3)²+(y-4)² = (0-1)²+(y-6)²

9 +y²-8y+16 = 1+ y²-12y+36

-8y+25 = -12y+37

-8y+12y= 37 -25

4y = 12

y = 3

o centro:

C(0, y) = (0, 3)......=> a=0...e....b=3

raio:

C....(0,.......3)

A....(3,.......4)

r² = (0-3)²+(3-4)²= (9) +(1) = 10

the reduzide equation:

(x-a)² +(y-b)² = r²

(x-0)² +(y-3)² = 10

x² + (y-3)² = 10 #