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The locus of the point of intersection of the tangents
\( \mathrm{P}^{12 i} \) to \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) at the ends whose eccentric angles

W differ by a right angle is
(1) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{1}{2} \)
(2) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\frac{1}{4} \)
(3) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=2 \)
(4) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=3 \)
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