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1. Show that the line with equation x-y=6 is a tangent to the curve with equation x^2-6x+y^2-2y+2=0

2. Let C be the curve with eq. 4x^2+9y^2=36. Find the exact value of K for which the line 2x+3y=k is a tangent to C.

3. Find the value or values of m for which the line y=mx is tangent to the curve x^2+2xy+2x=1.

4. Find the values of K for which the line y=2x-k is tangent to the curve with equation x^2+y^2=5

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