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A line tangent to a circle at any point on a circle is perpendicular to the line joining the point to the center of the circle.
The equation of the circle is x^2 + y^2 + 2y = 24
x^2 + y^2 + 2y = 24
=> x^2 + y^2 + 2y + 1 = 25
=> x^2 + (y + 1)^2 = 25
The center of this circle is (0, -1)
The line joining the points (0, -1) and (0, 4) is vertical. The line perpendicular to this is horizontal. The slope of a horizontal line is 0. The equation of a line with slope 0 passing through (0, 4) is y = 4.
The required equation of the tangent is y = 4.
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