Find the equation of the tangent at ( 0 , 2) to the circle with equation

Find the equation of the tangent at ( 0 , 2) to the circle with equation

 Find the equation of the tangent at ( 0 , 2) to the circle with equation

Answer：(x + 2)2 + (y + 1)2 = 13

(-2 , -1) : center of circle
m = (2 - -1) / (0 - -2) = 3 / 2 : slope of line through the center and the point of tangency (0 , 2)
The line through the center and the point of tangency (0 , 2) is perpendicular to the tangent.
M = -2 / 3 : slope of tangent
y = -(2/3)x + 2 : equation of tangent given its slope and point (0 , 2).