1. **State the problem:** Given the circle equation $$x^2 + y^2 - ax - by - 12 = 0$$ and the center of the circle is at point $(2,3)$, find the values of $a$ and $b$. 2. **Recall the formula for the center of a circle:** The general form of a circle is $$x^2 + y^2 + Dx + Ey + F = 0$$ where the center is $$\left(-\frac{D}{2}, -\frac{E}{2}\right)$$. 3. **Match the given equation to the general form:** Here, $D = -a$ and $E = -b$. 4. **Use the center coordinates:** Given center $(2,3)$, we have $$2 = -\frac{D}{2} = -\frac{-a}{2} = \frac{a}{2} \implies a = 4$$ $$3 = -\frac{E}{2} = -\frac{-b}{2} = \frac{b}{2} \implies b = 6$$ 5. **Final answer:** $$a = 4, \quad b = 6$$