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The differential equation satisfied by the system of parabolas \( y^{2}=4 a(x+a) \) is: [JEE Main-2021 (March)]
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(a) \( y\left(\frac{d y}{d x}\right)^{2}-2 x\left(\frac{d y}{d x}\right)-y=0 \)
(b) \( y\left(\frac{d y}{d x}\right)^{2}-2 x\left(\frac{d y}{d x}\right)+y=0 \)
(c) \( y\left(\frac{d y}{d x}\right)^{2}+2 x\left(\frac{d y}{d x}\right)-y=0 \)
(d) \( y\left(\frac{d y}{d x}\right)+2 x\left(\frac{d y}{d x}\right)-y=0 \)
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