1.write the equation of the circle with the radius of 10 and a center at (3,-1)

2. find the center and the radius of the circle represented by the equation 2x^2+2y^2+4x-8y-6=0

3. a lighthouse beacon will illuminate to a distance of 12 km. if the lighthouse is located at (-5,2) on a grid, find the equation of the location of the furthest points lit by the beacon.

1.
(x - 3)² + (y + 1)² = 10²

2.
2x² + 2y² + 4x - 8y - 6 = 0
x² + y² + 2x - 4y - 3 = 0
x² + 2x + 1 - 1 + y² - 4y + 4 - 4 - 3 = 0
Or x² + 2x + 1 is (x + 1)² and  y² - 4y + 4 is (y - 2)²
Then (x + 1)² + (y - 2)² - 8 = 0
(x + 1)² + (y - 2)² = 8
Or 8 = (2 * sqrt(2) )²
The center is I ( -1 , 2 ) and the radius is 2 * sqrt(2)

3.
It is like a circle and the furthest points are those who verify the equation of the circle (x + 5)² + (y - 2)² = 12²

I hope i helped

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