The nearest point on the circle $x^2+y^2-6x+4y-12=0$ from $\left(-5, 4\right)$ is 

$$\begin{gathered} Given circle x^2+y^2-6x+4y-12=0 \\ Centre\left(C\right)=(3,-2),r=5 \\ Given point P=(-5,4) \\ Now CP=10 \\ Nearest point divides CP in the rato CP-r : r =1:1 internally then \\ Required point=(\frac{3-5}{2},\frac{-2+4}{2})=(-1,1) \end{gathered}$$