If the line x = my + k touches the parabola x | vedclass

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(A) The given equation of the line is $x = my + k$,which can be rewritten as $x - my = k$. Substituting $x = my + k$ into the parabola equation $x^2 =

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$a/m$

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(A) The given equation of the line is $x = my + k$,which can be rewritten as $x - my = k$. Substituting $x = my + k$ into the parabola equation $x^2 = 4ay$: $(my + k)^2 = 4ay$ $m^2y^2 + 2mky + k^2 = 4ay$ $m^2y^2 + (2mk - 4a)y + k^2 = 0$ Since the line touches the parabola,the discriminant of this quadratic equation must be zero: $D = (2mk - 4a)^2 - 4(m^2)(k^2) = 0$ $4m^2k^2 - 16amk + 16a^2 - 4m^2k^2 = 0$ $-16amk + 16a^2 = 0$ $16amk = 16a^2$ $k = a/m$

If the line $x = my + k$ touches the parabola $x^2 = 4ay$,then $k = $

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