A satellite dish is in the shape of a parabolic surface. Signals coming from a s

Question

A satellite dish is in the shape of a parabolic surface. Signals coming from a satellite strike the surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish shown has a diameter of 6 feet and a depth of 3 feet. The parabola is positioned in a rectangular coordinate system with its vertex at the origin. a. Write an equation in the form y=ax2 for the parabola used to shape the dish. 6 feet Receiver Type an integer or a fraction.) b. The receiver should be placed at the focus (0,p). The value of p is given by the equation a How far from the base of the dish should the receiver be placed? (3,3) 3 feet Ap p =| | feet Type an integer or a decimal.)

Explanation / Answer

equation of parabola given as y = ax2

putting point (3,3) into equation we get

3= a(3)2

a=1/3

equation becomes

y = 1x2/3

value of P is given by equation a =1/4P

i.e 1/3 = 1/4P

4P=3

P=3/4

focus is at (0,P)

i.e (0,3/4)

The recievershould be placed at 3/4 feet or 0.75 feet from ground.

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