# What is the equation of the a circle passing through (-4, -4) and tangent to the line 2x - 3y +9=0 at (-3,1)?

If the circle has centre $\left(- 4 , - 4\right)$ and passes through $\left(- 3 , 1\right)$, then the radius has slope $\frac{1 - \left(- 4\right)}{- 3 - \left(- 4\right)} = 5$, but the line $2 x - 3 y + 9 = 0$ has slope $\frac{2}{3}$ so is not perpendicular to the radius. So the circle is not tangential to the line at that point.