Question

знайти ексцентриситет еліпса,якщо його осі відносяться як 13:5

Answer 1

$e = \sqrt{1-b^2/a^2} = \sqrt{1-5^2/13^2} = 12/13$

Answer 2

Finding the Eccentricity of an Ellipse

To find the eccentricity of an ellipse, we need to know the ratio of its major and minor axes. In this case, the ratio is given as 13:5.

The eccentricity of an ellipse can be calculated using the formula:

eccentricity (e) = √(1 - (b^2/a^2))

Where: - a is the length of the semi-major axis (half of the major axis) - b is the length of the semi-minor axis (half of the minor axis)

In this case, the ratio of the major and minor axes is 13:5. Let's assume the length of the semi-major axis is 13x and the length of the semi-minor axis is 5x.

Using the formula, we can calculate the eccentricity:

eccentricity (e) = √(1 - (5x^2)/(13x^2))

Simplifying the equation:

eccentricity (e) = √(1 - 25x^2/169x^2) eccentricity (e) = √(1 - 25/169) eccentricity (e) = √(144/169) eccentricity (e) = 12/13

Therefore, the eccentricity of the ellipse with a major-to-minor axis ratio of 13:5 is 12/13.

Please note that the above calculation assumes that the ellipse is centered at the origin (0,0) and is not rotated. If the ellipse is rotated or translated, additional calculations may be required.