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Sagot :
The equation of ellipse is [tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex] and height of arch is 5.77 feet
Assume that the center of the ellipse is at the origin.
So, The general equation for an ellipse is:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Where:
x is Horizontal distance, in feet.
y is Vertical distance, in feet.
a is Horizontal semiaxis length (half-width), in feet.
and b is Vertical semiaxis length (height), in feet.
According to the question,
x = 3 , a = 11 and b = 6
Putting all the values ,
So , the equation of ellipse will be
[tex]\frac{x^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Putting x = 3,
[tex]\frac{3^2}{11^2} + \frac{y^2}{6^2} = 1[/tex]
Solving for y,
[tex]\frac{y^2}{36} = 1 - \frac{9}{121}[/tex]
=> [tex]y^2 = \frac{(121 - 9)36}{121}[/tex]
=> y² = 4032 / 121
=> y = √33.32
=> y = 5.77 feet
To know more about Ellipse here
https://brainly.com/question/14281133
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