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The line $y=m x+c$ touches the parabola $x^2=4 a y$, if
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The correct answer is:
$c=-a m^2$
$x^2=4 a(m x+c) \Rightarrow x^2-4 a m x-4 a c=0$
It touches, then $B^2-4 A C=0$ (discriminant \(\mathrm{D}=0\)).
$\Rightarrow 16 a^2 m^2+16 a c \Rightarrow a c=-a^2 m^2 \Rightarrow c=-a m^2$
It touches, then $B^2-4 A C=0$ (discriminant \(\mathrm{D}=0\)).
$\Rightarrow 16 a^2 m^2+16 a c \Rightarrow a c=-a^2 m^2 \Rightarrow c=-a m^2$
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