Question

A searchlight uses a parabolic mirror to cast a beam of light in parallel rays where the light bulb is located at the focus of the parabola in order to give the best illumination. The mirror is modeled by y^2=36(x-10), where the measurements are in cm. What is the location of the light bulb?

Answer 1

Answer:

the third option

Step-by-step explanation:

Our equation is

${y}^{2} = 36(x - 10)$

Equation of a vertical parabola is

$( {y - k)}^{2} = 4p(x - h)$

where (h,k) is the center

The focus is

(h+p, k)

Equation of directrix is

x= h-p,

Here the center is (10,0)

Next, we factor out 4 in the original equation

$4(9)$

So we have

${y}^{2} = 4(9)(x - 10)$

So our p=9,

So our focus is

(10+9,0) or (19,0)

The third option is the answer