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For what values of slope m does the line y = m(x - a) intersect the parabola y² = 4ax in two distinct real points?

1. m in R
2. m in [-1, 1]
3. m in R - {0}
4. m in (-infinity, 1] union [1, infinity)

Correct answer: m in R - {0}

Solution

The line passes through the focus (a,0); any non-horizontal focal line cuts the parabola in two distinct points, so the condition is m != 0 (m = 0 gives the axis, a single intersection at vertex... actually a tangent/double).

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