English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

9x^2+4y^2-72x-24y=0

2007-04-28 17:13:43 · 3 answers · asked by Anonymous in Science & Mathematics Mathematics

3 answers

9x^2 + 4y^2 - 72x - 24y = 0
9x^2 - 72x + 4y^2 - 24y = 0
9(x^2 - 8x) + 4(y^2 - 6y) = 0
9(x^2 - 8x + 16) + 4(y^2 - 6y + 9) = 0 + 9*16 + 4*9
9(x - 4)^2 + 4(y - 3)^2 = 180
(9/36)(x - 4)^2 + (4/36)(y - 3)^2 = 180/36
(1/4)(x - 4)^2 + (1/9)(y - 3)^2 = 5
(1/20)(x - 4)^2 + (1/45)(y - 3)^2 = 1

2007-04-28 17:43:50 · answer #1 · answered by Helmut 7 · 0 0

9x^2 + 4y^2 - 72x - 24y = 0
9x^2 - 72x + 4y^2 - 24y = 0
(9x^2 - 72x) + (4y^2 - 24y) = 0
9(x^2 - 8x) + 4(y^2 - 6y) = 0
9(x^2 - 8x + 16 - 16) + 4(y^2 - 6y + 9 - 9) = 0
9((x - 4)^2 - 16) + 4((y - 3)^2 - 9) = 0
9(x - 4)^2 - 144 + 4(y - 3)^2 - 36 = 0
9(x - 4)^2 + 4(y - 3)^2 - 180 = 0
9(x - 4)^2 + 4(y - 3)^2 = 180
(((x - 4)^2)/4) + (((y - 3)^2)/9) = 5

to make this look like the ellipse formula

(((x - 4)^2)/20) + (((y - 3)^2)/45) = 1

a^2 + b^2 = c^2
20 + 45 = c^2
c^2 = 65
c = sqrt(65)

Eccentricity = sqrt(65)/sqrt(20) = sqrt(13/4) = (1/2)sqrt(13)

Center : (4,3)
Eccentricity : sqrt(13)/2

2007-04-29 00:48:30 · answer #2 · answered by Sherman81 6 · 0 0

Complete the square:

9(x^2 - 8x) + 4(y^2 - 6y) = 0
9(x^2 - 8x + 16) + 4(y^2 - 6y + 9) = 144 + 36
9(x-4)^2 + 4(y-3)^2 = 180

(x-4)^2 / 20 + (y-3)^2 / 45 = 1

The center is at (4, 3) and a = sqrt(45) and b = sqrt(20). c = sqrt(25) = 5. The major axis is vertical.

2007-04-29 00:20:27 · answer #3 · answered by Ken M 3 · 0 0

fedest.com, questions and answers