The radar detects planes in a parabolic direction. It has a height of 30 meters and the document provides information to calculate the diameter of the radar disk and distance of the transmitter from the base if the height is 6 meters. Using the formula (x-h)2 = 4p(y-k) and given points, the radius is calculated to be approximately 13.86 meters. For a plane 5482km high and 15km from the radar, the maximum reach of the radar is around 13.24474km so the plane cannot send or receive signals.

1. CONICS
A radar pointing 90 degrees to the sky can detect signals from
planes in a parabolic direction. It has 30 m height from the base of
the radar disc to the ground.
a) Find the diameter of the radar disk and the distance of
transmitter from the base of the disk if the height of the disk is
6 meters and some parts of it measures 16 m wide and 2 m
height?
b) If there's a plane flying 5482km high and 15 km from the radar
can the plane send a signal to the radar or vice versa?

2. Solution
A)
We all know that it is a vertical parabola opening up. The formula is (x-h)2 = 4p (y-k).
In graphing consider the base of the radar is on the origin (0,0). Then substitute the
given measurements.
Were looking for p, get the focus (transmitter) first. Use the given points 2 ( 2 m
high) and 8 m radius of the given point (16 m wide).
given: x=8 Solution: (x-h)2 = 4p (y-k)
y=2 (8-0)2=4p (2-0)
(h,k)= (0,0) (8)2=4p (2)
64=8p
=p
8=p

3. •These are the points that are given.
•(-8,2) and (8,2) are the given
coordinates.
•Those points are only parts of the
radar disk.

4. To get the focus add the value of p to k. Use the formula again then
substitute the given values. Using the original height of the radar disk
which is 6 meters you will find the radius of the radar.
(x-h)2 = 4p (y-k)
(x-0)2 = 4(8)(6-k)
X2=4(8)(6)
X=
X 13.86
So the radius of the radar
Graph of the
disk is approximately
radar disk
13.86 meters. And the
height of the focus is 8 m.

5. B)
using the same formula (x-h)2 = 4p (y-k) we can find out if the plane can
send signal or receive.
Note: subtract 30 m for the height of the radar from the base of the disk
to the ground.
Given: y(height of the plane)=5482 km-30 m
=5482000 m-30m
=5481970 m
p=8
x=?(unknown)
(h,k)= (0,0) Conclusion:
Solution: The plane can’t receive or send any
(x-h)2 = 4p (y-k) signal to the radar because the maximum
reach of the radar is approximately 13.24474
(x-0)2 = 4(8)(5481970)
km and the plane is 15 km from the radar.
x2 = 175423040
x=
x 13244.74 m
x 13.24474 km