EDB — 1QC

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[1QC]For each point \((x,y)\) of the plane with \(x,y{\gt}0\) passes a single ellipses \(4 x^ 2 + y^ 2 = a\) (with \(a{\gt}0\)). Describe the family of curves that at each point are orthogonal to the ellipse passing through that point. See figure 12.

Solution 1

[1QF]

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Figure 6 Ellipses (in red) and curves orthogonal to them.

[ [1QG]]

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