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Paragraph Questions:
P
An ellipse whose distance between foci \( S \) and \( S^{\prime} \) is 4 units
W is inscribed in the \( \triangle A B C \) touching the sides \( A B \), \( A C \) and \( B C \) at \( P, Q \) and \( R \), respectively. If centre of ellipse is at origin and major axis along \( X \)-axis, \( S P+S^{\prime} P=6 \)
If \( A B=B C \) and \( \angle B=\pi / 2 \), then locus of \( A \) is
(1) \( \left(x^{2}+y^{2}-14\right)^{2}=4\left(5 x^{2}+9 y^{2}-45\right) \)
(2) \( \left(x^{2}+y^{2}-14\right)^{2}=4\left(5 x^{2}+9 y^{2}-54\right) \)
(3) \( \left(x^{2}+y^{2}-14\right)^{2}=4\left(9 x^{2}+5 y^{2}-45\right) \)
(4) \( \left(x^{2}+y^{2}-14\right)^{2}=4\left(9 x^{2}+5 y^{2}-54\right) \)
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