The potential in an electric field varies as (V=(x^2-y^2)). The...

The potential in an electric field varies as, (V=\left(x^2-y^2\right)) (\therefore) Electric field, ($$\begin{aligned} E & =-\left[\frac{d v}{d x} \hat{\mathbf{i}}+\frac{d v}{d y} \hat{\mathbf{j}}\right] \quad[\because E=\Delta V] \\ & =-\left[\frac{d}{d x}\left(x^2-y^2\right) \hat{\mathbf{i}}+\frac{d}{d y}\left(x^2-y^2\right) \hat{\mathbf{j}}\right] \\ E & =-[2 x \hat{\mathbf{i}}-2 y \hat{\mathbf{j}}] \Rightarrow E=-2 x \hat{\mathbf{i}}+2 y \hat{\mathbf{j}} \end{aligned}$$) Expression of the electric field is linear equation in two variables, i.e. straight lines in $X-Y$ plane and slope having (45^{\circ}, 35^{\circ}) etc. Hence, the option (c), represents correct graph.