The line from point of contact to centre is radius. If this line (radius) is perpendicular to the given line 2x + 3y =6, then this given line is tangent.

Now

Centre = (4, -5)

Point of contact=(6, -2)

slope of radius

Slope of given line 2x + 3y = 6 is

Product of their slopes

So, the given line is perpendicular to the radius at the point of contact.

so, it is a tangent at rhe point of contact.