Use implicit differentiation to find the points where the circle defined by
x^{2}+y^{2}-6x-4y = -9
has horizontal and vertical tangent lines. I found the implicit derivative without a hitch but how do I use it to find x?

Question

Use implicit differentiation to find the points where the circle defined by
x^{2}+y^{2}-6x-4y = -9
has horizontal and vertical tangent lines. I found the implicit derivative without a hitch but how do I use it to find x?

anonymous · Answer

ok, I see what's going on.

anonymous · Answer

The circle will have 2 vertical and 2 horizontal tangent lines
If you rearrange the equation to fit the canonical circle equation, which is $$(x - center_x)^{2}+(y - center_y)^{2} = radius ^{2}$$ 
you have
$$(x-3)^{2}+(y-2)^{2}=4$$
This is a circle of radius 2 centered at (3,2)|dw:1381194060291:dw|