Conics

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Conics

  1. 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. 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. 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. 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. 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

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