If \( a \neq 0 \) and the line \( 2 b x+3 c y+4 d=0 \) passes through the points of intersection...

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If \( a \neq 0 \) and the line \( 2 b x+3 c y+4 d=0 \) passes through the points of intersection of the parabolas \( y^{2}=4 a x \)
\( \mathrm{P} \) and \( x^{2}=4 \) ay, then

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(a) \( d^{2}+(2 b+3 c)^{2}=0 \)
(b) \( d^{2}+(3 b+2 c)^{2}=a^{2} \)
(c) \( d^{2}+(2 b-3 c)^{2}=0 \)
(d) \( d^{2}+(2 b+3 c)^{2}=a^{2} \)
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