The condition for which the straight line y = | vedclass

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(A) The equation of the parabola is $y^2 = 4ax$. Substituting $y = mx + c$ into the parabola equation: $(mx + c)^2 = 4ax$ $m^2x^2 + 2mcx + c^2 - 4ax =

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$c = a/m$

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(A) The equation of the parabola is $y^2 = 4ax$. Substituting $y = mx + c$ into the parabola equation: $(mx + c)^2 = 4ax$ $m^2x^2 + 2mcx + c^2 - 4ax = 0$ $m^2x^2 + (2mc - 4a)x + c^2 = 0$. For the line to touch the parabola,the discriminant of this quadratic equation must be zero: $D = (2mc - 4a)^2 - 4(m^2)(c^2) = 0$ $4m^2c^2 - 16amc + 16a^2 - 4m^2c^2 = 0$ $-16amc + 16a^2 = 0$ $16a^2 = 16amc$ $a = mc$ $c = a/m$. Thus,the correct condition is $c = a/m$.

The condition for which the straight line $y = mx + c$ touches the parabola $y^2 = 4ax$ is

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