Answer:
75 cm
Explanation:
You want to know the length of the struts between the edge of a parabolic dish 120 cm in diameter and 15 cm deep, and the collector at the focus of the dish.
Equation
The equation of a parabola with its vertex at the origin and passing through points (±60, 15) can be written as ...
y/15 = (x/60)² . . . . parabola scaled vertically by 15, horizontally by 60
240y = x² . . . . . . multiply by 3600
4(60)y = x² . . . . . factor out 4 from the coefficient of y
Focus
This equation is of the form ...
4py = x²
where p = 60 is the distance from the vertex to the focus. Since the dish is 15 cm deep, the focus lies 60-15 = 45 cm above the edge of the dish.
Struts
The length of each strut from the edge of the dish to the focus will be the hypotenuse of a right triangle with legs 45 and 60. The Pythagorean theorem tells us that length is ...
c² = a² +b²
c = √(a² +b²) = √(45² +60²) = 15√(9+16) = 75
The length x of each strut is 75 cm.