gre geometry question of 170 score level

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i m thinking c is _2 And B is 2 and A point is we can find , but i am using no method only assumptions

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Since $k\gt 0$, solving $k-x^2=0$ for $x$ gives us $$B(\sqrt k,0), \ \ C(-\sqrt k,0).$$ Hence, with $A(0,k)$, we have $$\frac 12\times k\times \left(\sqrt k-\left(-\sqrt k\right)\right)=\frac 18\Rightarrow k\sqrt k=\frac 18$$$$\Rightarrow \left(k\sqrt k\right)^2=\left(\frac 18\right)^2\Rightarrow k^3=\frac{1}{4^3}\Rightarrow k=\frac 14.$$