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Two straight lines (y-b)=m1(x+a) and (y-...

Two straight lines `(y-b)=m_1(x+a)` and `(y-b)=m_2(x+a)` are the tangents of `y^2=4a x.` Prove `m_1m_2=-1.`

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Clearly, both the lines pass through (-a,b), which is a point lying on the directrix of the parabola.
Thus, `m_(1)m_(2)=-1`, because tangents drawn from any point on the directrix are always mutually perpendicular.
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