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Parabola and Tangent Lines

The parabola y= x^2+4 has two tangents which pass through the point (0,-2). One is tangent to the parabola at (a, a^2+4) and the other at (-a, a^2+4) where a is a certain positive number. The question is a=?

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According to definition, the slope of the tangent line to a function (parabola) is the first derivative of that function (parabola).

We calculate the first derivative of the parabola. The derivative ...

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The solution provides a detailed and step-by-step explanation for the problem.