A lab designed a radio telescope with a diameter of 300 feet and a maximum depth of 38 feet. A graph depicts a cross section of this telescope. What is the equation of this parabola, given that...

A lab designed a radio telescope with a diameter of 300 feet and a maximum depth of 38 feet. A graph depicts a cross section of this telescope. What is the equation of this parabola, given that the points lying along the right and left are (-150,38) and (150,38).

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The radio telescope designed by the lab has a diameter of 300 feet and a maximum depth of 38 feet.

The equation of the parabola representing the cross section of the telesope has to be determined given that the points (-150, 38) and (150, 38) lie on it.

The equation is of the form y = ax^2. Substituting the co-ordinates of any of the points given:

38 = a*150^2

=> a = `19/11250`

The required equation of the parabola is `y = (19/11250)*x^2`

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