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sesenic [268]
3 years ago
7

A rectangular board is 18 feet by 24 feet. How far from the center of the board should the foci be located in order to cut the l

argest elliptical tabletop from the board?
a. 7.94 ft
b. 4.06 ft
c. 15 ft
d. 15.9 ft
Mathematics
1 answer:
solniwko [45]3 years ago
7 0

<span>x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b

Center (0, 0):

h = 0
k = 0

a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:

General : (x - h)² / a² + (y - k)² / b² = 1

(x - 0)² / (12)² + (y - 0)² / (9)² = 1

x² / 144 + y² / 81 = 1


Focus = c:
        _____
c = √a² - b²
        _______
c = √(12)² - (9)²
        ______
c = √144 - 81 = sqrt63 = 7.9372</span>

Focus : ( -7.9372, 0) and ( 7.9372, 0)


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