Mathematics

Mathematics

Problem

An ellipse has a semi-major axis of length

a

and semi-minor axis

b

. A vertical line

x = k

(where

0 < k < a

) intersects the ellipse at point

P

and the auxiliary circle at point

Q

in the first quadrant. If the

y

-coordinate of

Q

is

12\,\text{units}

and the

y

-coordinate of

P

is

8\,\text{units}

, determine the eccentricity of the ellipse.

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