A Straight line passing through a fixed point $\left(3,5\right)$ and intersects coordinate axis at point $A$and $B$.

Let coordinates of $A\left(p,0\right)$ and $B\left(0,q\right)$

$\therefore$Intercept form of line is $\frac{x}{p}+\frac{y}{q}=1$

Here, point $\left(3,5\right)$will satisfy the line.

$\Rightarrow \frac{3}{p}+\frac{5}{q}=1$

Here, coordinate of point are $C(x,y)=(p,q)$

Hence, to find locus of $C$ substitute $p=x \& q=y$ in the above equation.

$\Rightarrow \frac{3}{x}+\frac{5}{y}=1$

$\Rightarrow 5x+3y-xy=0$

Now compare $ax+by+2hxy=0$to $5x+3y-xy=0$

$a=5 b=3, h=-\frac{1}{2}$

$a+b+h \Rightarrow 5+3-\frac{1}{2}=\frac{15}{2}$.