Right answer is (d) Elliptic
Explanation: The general equation is in this form.
\(A\frac{\partial ^2 \Phi}{\partial x^2}+B\frac{\partial ^2 \Phi}{\partial x\partial y}+C\frac{\partial^2\Phi}{\partial y^2}+D\frac{\partial\Phi}{\partial x}+E\frac{\partial \Phi}{\partial y}+F\Phi +G=0\)
Comparing \(\frac{\partial^2 \Phi}{\partial x^2}+\frac{\partial ^2 \Phi}{\partial y^2}=0\) with the above equation,
A=1
B=0
C=1
To find the type,
d=B^2-4AC
d=-4
As d is negative, Laplace’s equation is elliptical.