The coordinates of point $P$ are $\left(a,b\right)$ where a is root of the equation $x^2+x-42=0$ and $b$ is integral root of the equation $x^2+ax+\left(a^2-37\right)=0$ . The coordinates $P$ can be

If $a=-7,x^2-7x+12=0\Rightarrow x=4,3$

$\therefore P=\left(-7,4\right)\left(or\right)\left(-7,3\right)$

If $a=6,x^2+6x-1=0,\Delta =36+4=40>0$  and not a perfect square

$\therefore$  Roots are irrational

$\therefore \text{'}b\text{'}$  does not exist in this case

$\therefore P=\left(-7,4\right)\left(or\right)\left(-7,3\right)$