If the coordinate of one end of a diameter of the circle having equation x^2+y^2+4x-6y+8=0 is (0,2) then find the coordinate of the other end of the diameter

 (-4, 4)

Step-by-step explanation:

Given: x² + 4x    +  y² - 6y      = -8

Complete the square:  x² + 4x + 4 +  y² - 6y + 9 = -8 + 4 + 9

                                  →     (x + 2)²   +      (y - 3)²    =     5

Center: (-2, 3)

Since one end point of the circle is (0, 2) and the other end point must pass through endpoint (0, 2) and the center (-2, 3), find the slope ...

m = down 1 and right 2

The other endpoint will be:  UP 1 and LEFT 2 from the center

→ (-2 - 2, 3 + 1)    =   (-4, 4)

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option