Answer:
Equation of parabola is x² = 225y
Step-by-step explanation:
General equation of a parabola symmetric about y axis is given by x² = 4ay
Here it is given that the glass dome will be 60 feet in diameter and will have a depth of 4 feet.
That is at x = 30 value of y is 4.
Substituting
30² = 4 x a x 4
900 = 16 a
[tex]a=\frac{225}{4}[/tex]
Equation of parabola
[tex]x^2=4\times \frac{225}{4}\times y=225y\\\\x^2=225y[/tex]
Equation of parabola is x² = 225y
The equation of the parabolic cross-section of the dome is; y² = (16/30)x
The standard equation of a parabola is given by;
y² = 4ax
We are told that the glass dome will be 60 feet in diameter and will have a depth of 4 feet.
Thus;
x = 60/2 = 30 and y = 4
Thus;
4² = 4(a * 30)
16 = 120a
a = 4/30
Thus;
Equation of parabola is;
y² = (16/30)x
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