If the line y = mx + c is a tangent to the pa | vedclass

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(A) The equation of the tangent to the standard parabola $y^2 = 4ax$ with slope $m$ is given by $y = mx + \frac{a}{m}$.The given parabola is $y^2 = 4a

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$c$

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(A) The equation of the tangent to the standard parabola $y^2 = 4ax$ with slope $m$ is given by $y = mx + \frac{a}{m}$.The given parabola is $y^2 = 4a(x + a)$.By shifting the origin to $(-a, 0)$,the equation becomes $Y^2 = 4aX$,where $Y = y$ and $X = x + a$.The tangent to $Y^2 = 4aX$ is $Y = mX + \frac{a}{m}$.Substituting back $Y = y$ and $X = x + a$,we get $y = m(x + a) + \frac{a}{m}$.Expanding this,we have $y = mx + ma + \frac{a}{m}$.Comparing this with the given line $y = mx + c$,we get $c = ma + \frac{a}{m}$.Therefore,$ma + \frac{a}{m} = c$.

If the line $y = mx + c$ is a tangent to the parabola $y^2 = 4a(x + a)$,then $ma + \frac{a}{m}$ is equal to

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