9x2 + 4y2 = 36

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Given an ellipse of:

9x² + 4y² = 36

Calculate the following:

• x and y intercepts
• Coordinates of the foci
• Length of the major and minor axes
• Eccentricity (e)

Standard ellipse equation

Find square roots of denominator:

Calculate x intercept by setting y = 0:

x² = 4 x 1

x² = 4

x = √4

x = ± 2

Calculate y intercept by setting x = 0:

y² = 9 x 1

y² = 9

y = √9

y = ± 3

Calculate the foci:

c² = √a² - b²

Since a must be greater than b:

a = 3 and b = 2

c² = √9² - 4²

c² = √5

Foci Points are (0,√5) and (0,-√5)

Calculate length of the major axis:

Major axis length = 2 x a

Major axis length = 2 x 3

Major axis length = 6

Calculate length of the minor axis:

Minor axis length = 2 x b

Minor axis length = 2 x 2

Minor axis length = 4

Calculate the area of the ellipse:

Area = πab

Area = π(4)(9)

Area = 36π

Calculate eccentricity (e):

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Tags:

• eccentricity
• ellipse
• focus