Mathematics - Parabola Question with Solution | TestHub

The focus of the parabola is $(1,0)$, so the diagonals are focal chords. With focal chord length $a(t+1/t{)}^2\dots$ solving gives $t=\pm 1/2$ and $t=\pm 2$, so the vertices are $A=(1/4,1)$, $B=(4,4),C=(4,-4),D=(1/4,-1).\mathrm{AD}=2,\mathrm{BC}=8$, distance between them = $15/4$. Area $=\frac{1}{2}(2+8)\cdot \frac{15}{4}=\frac{75}{4}$ sq.units.