MATH SOLVE

6 months ago

Q:
# 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 largest elliptical tabletop from the board?a. 7.94 ftb. 4.06 ftc. 15 ftd. 15.9 ft

Accepted Solution

A:

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

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