The locus of mid-points of the line segments joining \( \mathrm{P} ...

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The locus of mid-points of the line segments joining
\( \mathrm{P} \) \( (-3,-5) \) and the points on the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 \) is:

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(1) \( 9 x^{2}+4 y^{2}+18 x+8 y+145=0 \)
(2) \( 36 x^{2}+16 y^{2}+90 x+56 y+145=0 \)
(3) \( 36 x^{2}+16 y^{2}+108 x+80 y+145=0 \)
(4) \( 36 x^{2}+16 y^{2}+72 x+32 y+145=0 \)
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