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# The equation of common tangent to the parabolas y^{2} = 4ax and x^{2} = 4by is

- a
^{1/3}x + b^{1/3}y + (ab) = 0
- a
^{1/3}x + b^{1/3}y + (ab)^{2/3} = 0
- b
^{1/3}x + a^{1/3}y + (ab)^{1/3} = 0
- b
^{1/3}x – a^{1/3}y – (ab)^{1/3} = 0

^{1/3}x + b^{1/3}y + (ab) = 0^{1/3}x + b^{1/3}y + (ab)^{2/3}= 0^{1/3}x + a^{1/3}y + (ab)^{1/3}= 0^{1/3}x – a^{1/3}y – (ab)^{1/3}= 0## The correct answer is: a^{1/3}x + b^{1/3}y + (ab)^{2/3} = 0

### Tangent of parabola y^{2} = 4ax is y = mx + a/m, which also touches to the parabola x^{2 }= 4by a/m = – bm^{2}m = –(a/b)^{1/3}

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