Mathematics

Problem

A graphic designer is creating a logo by vertically compressing a circle of radius

10\,\text{cm}

into an ellipse. A point

Q

on the original circle (auxiliary circle) is at a distance of

6\,\text{cm}

from the vertical

y

-axis. The corresponding point

P

on the resulting ellipse is at a distance of

5\,\text{cm}

from the horizontal

x

-axis. Find the length of the minor axis of the ellipse.