Given an ellipse of:

9x^{2} + 4y^{2} = 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:

x^{2} = 4 x 1

x^{2} = 4

x = √4

x = ± 2

Calculate y intercept by setting x = 0:

y^{2} = 9 x 1

y^{2} = 9

y = √9

y = ± 3

Calculate the foci:

c^{2} = √a^{2} - b^{2}

Since a must be greater than b:

a = 3 and b = 2

c^{2} = √9^{2} - 4^{2}

c^{2} = √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):

e = √a^{2} - b^{2} √a^{2}

e = √9^{2} - 4^{2} √9^{2}

e = 0.89580641647762

How does the Ellipses Calculator work?
Free Ellipses Calculator - Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity. This calculator has 3 inputs.

What 3 formulas are used for the Ellipses Calculator?
(x

^{2} /a

^{2} ) + (y

^{2} /b

^{2} ) = 1

c

^{2} = sqrt(a

^{2} - b

^{2} )

Area = πab

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What 3 concepts are covered in the Ellipses Calculator?
eccentricity Deviation of a conic from a circular shape ellipse a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant focus fixed point on the interior of a parabola used in the formal definition of the curve

Example calculations for the Ellipses Calculator
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