Statement 1: y=mx−m1 is always a tangent to the parabola y2=−4x for all non-zero values of m.
Statement 2: Every tangent to the parabola y2=−4x will meet its axis at a point whose abscissa is non-negative.
Solutions · 1
Official solution
For y2=−4ax (a=1), the line y=mx−ma=mx−m1 is indeed always tangent (a standard tangent-condition identity), so Statement 1 is true.
A tangent to y2=−4x meets the axis (y=0) at x=m21≥0, so Statement 2 is also true, but it does not directly explain why Statement 1's specific line is a tangent --- it is a separate, true observation.