Question

.
A sound recieving dish wand at out door sporting events is Constructed in
the shape of paraboloid with its focus 5
inches the vertex. Determine the exact width (in inches) of the dish if the depth is to be 2 feet.​

Answer 1

Answer:

w≅8.46ft

Data

focus=8

vertex=(0,0)

width=?

depth (y)=3ft

parabola equation: (x-h)^{2}=4p(y-k)(x−h),

then for V=(0,0), x^{2} =4py

x² =4py , be focus(f)=8in;

x^{2} =4*8*y=32y then y = x²/32

we have that y=3ft then 3=x²/32

but 1in≅0.083ft so x^{2} =3*32*0.083=7.968

x=±2.82, finally w=3*2.82≅8.46ft