$$ \frac{x^2}{a}+\frac{x y}{h}+\frac{y^2}{b}=0(a \neq 0, h \neq 0, b \neq 0) $$ represents two coincident if

Given, $\frac{x^2}{a}+\frac{x y}{h}+\frac{y^2}{b}=0$ $$ b h x^2+a b x y+a h y^2=0 $$ Two equations are coincident when the ratio of each coefficients is same. Then, the two required lines are same. $$ \begin{aligned} & \text { So, }(y-m x)=0 \\ & \Rightarrow(y-m x)^2=0 \\ & y^2+m^2 x^2-2 m x y=0 \end{aligned} $$ Compare (i) \& (ii) $$ b h=m^2 \text { and }-2 m=a b, a h=1 $$ Take $-2 m=a b$ and square both sides $$ \begin{aligned} & 4 m^2=a^2 b^2 \\ & 4(b h)=a^2 b^2 \\ & 4 \mathrm{~h}=a^2 b \end{aligned} $$ Here, $a=\frac{1}{h}$ Then, $4 h=a \times \frac{1}{h} \times b$ $$ 4 h^2=a b $$ Therefore, option (b) is correct.