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Statement 1: y = mx - 1/m is always a tangent to the parabola, y^2 = -4x for all non-zero values of m. Statement 2: Every tangent to the parabola, y^2 = -4x will meet its axis at a point whose abscissa is non-negative.

1. Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
2. Statement 1 is false, Statement 2 is true.
3. Statement 1 is true, Statement 2 is false.
4. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

Correct answer: Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

Solution

Statement 1 is true because the line described will always intersect the parabola at exactly one point for any non-zero m, confirming it as a tangent. Statement 2 is also true since all tangents to the given parabola intersect the x-axis at non-negative x-values, but it does not explain why the line in Statement 1 is a tangent.

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