Question

brainliest for the CORRECT Answer

Answer 1

I like these conic questions; more challenging than the typical Brainly fare.

The cross section of our parabolic reflector dish through the center is, well, a parabola.  

We might as well put the vertex of the parabola at the origin and go with the simplest equation form for our parabola,

$y = ax^2$

A diameter of 10 means a radius of 5.  That corresponds to the x value.

The depth of 4 corresponds to the y value.

So this is telling us (5,4) is on our parabola.  We substitute and solve for a.

$4 = a(5^2)$

$a = \dfrac{4}{25}$

The rest of the verbiage asks for focus of the parabola.  

The focus of a parabola of this form is

$(0, \frac{1}{4a})$

so the distance from the vertex to the origin of 1/4a =  25/16.

Answer:  25/16 inches, which is exactly 1.5625 inches