Equation of Tangent Line for Curve at (5,-3)

[koolkris623]

Find the equation of the line tangent to the curve at (5, -3)
(x-2)^2 + (y+3)^2 = 9

I solved the derivative to be dy/dx = ((-2x+4)/ (2y+6))

when i plugged in the points (5, -3) I got the slope as -6/0...How is this possible??
How can i find the equation of this curve if the slope is undefined??

 

[rock.freak667]

If the gradient is undefined then, the tangent is vertical line e.g.x=1

btw: that curve, represents a circle with radius 3 and centre (2,-3) so if you are still confused about it, just make a sketch and see

 

[koolkris623]

wait if its a circle then why isn't the equation x = 5?

 

[rock.freak667]

The equation is x=5, I just used x=1 as an example of what the equation of a line with an undefined gradient looks like