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Finding the tangent to a curve

Find the condition that the curve y = mx + c to be a tangent to the parabola y^2 = 4 ax and also determine the point of contact.

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Let (x1, y1) be the point where the line

y = mx + c .........(1)

touches the parabola y^2 = 4ax ....(2)

But the equation of the tangent at (x1, y1) to the ...

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A thorough answer with all mathematical steps.