Answer:
The last option is the correct one.
Explanation:
x^2 + y^2 - 2x + 3y - 4 = 0
We can do this by first converting to the standard form.
x^2 - 2x + y^2 + 3y = 4
Completing the square on the x and y terms:
(x - 1)^2 - 1 + (y + 3/2)^2 - 9/4 = 4
(x - 1)^2 + (y + 3/2)^2 = 4 + 1 + 9/4
(x - 1)^2 + (y + 3/2)^2 = 29/4
Now compare this with the standard form
(x - a)^2 + (y - b)^2 = r^2 where (a, b) is the centre and r = the radius. So the centre is ((1, -3/2) and the radius = (√29)/2