jmc

Dividing by 2, we get $$x^2+y^2+5x-3y-9=0.$$Completing the square in $x$ and $y,$ we get $${\left(x+\frac{5}{2}\right)}^2+{\left(y-\frac{3}{2}\right)}^2=\frac{35}{2},$$so the area of the circle is $\boxed{\frac{35}{2}\pi }.$