What is the equation of the line tangent to the circle x^2 + y^2 + 2y = 24 at the point (0, 4)

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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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