Consider the points P(4k, 4k) and Q(4k,-4k) lying on the parabola y^{2}=4kx. If the vertex is A, then what is \angle PAQ equal to?

Explanation

The vertex of the parabola y^2=4kx is A(0,0). The slope of the line segment AP is m_1 = \frac{4k-0}{4k-0} = 1. The slope of the line segment AQ is m_2 = \frac{-4k-0}{4k-0} = -1. Because the product of their slopes is m_1 m_2 = 1 \times (-1) = -1, the lines AP and AQ are perpendicular. Thus, the angle \angle PAQ is 90^{\circ}.

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