If a horizontal ellipse touches the X-axis and Y-axis in the first quadrant, and this ellipse is rotated in anti-clockwise sense always touching the X-axis and Y-axis, till the ellipse becomes vertical for the first time , then why will always the centre of the ellipse be at a constant distance from the origin throughout the rotation?
2026-03-28 12:15:49.1774700149
Distance of centre of an ellipse touching both the positive X and Y axes from origin when the ellipse is being rotated
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This is true because the locus of intersection points of orthogonal tangents to an ellipse is a circle (called orthoptic of the ellipse).
It is centered at the center of the ellipse, and its radius is $\sqrt{a^2+b^2}.$
See also https://en.m.wikipedia.org/wiki/Ellipse#Tangent
or
https://en.m.wikipedia.org/wiki/Orthoptic_(geometry)