Answer
$1.4\ m$
Work Step by Step
Step 1. Assuming the top of the ceiling is the origin, we can write the equation of the parabola as $x^2=4py$
Step 2. As point $(\frac{15}{2}, -10)$ is on the curve, we have $(\frac{15}{2})^2=4p(-10)$. Thus $p =- \frac{45}{32}\approx-1.4$
Step 3. The light source should be placed at the focus, which is about $1.4\ m$ down from the top of the dome.
