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).
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`