Answer to Question #6512 in Analytic Geometry for mark joboy cantos

Question

the axial cross section of a head light reflector is a parabola with the bulbs center as focus. find the depth of the headlight in centimeters, if the bulbs center is 2 centimeter. from the vertex and the radius of the head light is 10 centimeter

Answer 1

Let's find the equation of parabola in a form y² = 2px. The vertex coordinates are V(0,0). We know that focus has coordinates F(2=p/2,0), so p=2*2 = 4 and we got y² = 2*4*x = 8x. Let's find the depth of the headlight:
y = 10 (the radius of the headlight)
y² = 100 = 8*x ==> x = 100/8 = 12.5cm.