# Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus?

I'm getting 8/5 ft. Is this correct? Appreciated!

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$1.6$ is the answer you seek. A convenient equation of the parabola is $5x^2=32y$. The line $x=y$ intersects the parabola at $(0\mid 0)$ -- trivial -- and at $(6.4\mid 6.4)$. One quarter of $6.4$ is $1.6$.