The locus of the point of intersection of perpendicular tangents to a parabola is the directrix of the parabola. This locus is called director circle even though it is a line.
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The locus of the point of intersection of perpendicular tangents to a parabola is the directrix of the parabola. This locus is called director circle even though it is a line.
The locus of the point of intersection of perpendicular tangents to a parabola is the directrix of the parabola. This locus is called director circle even though it is a line.
The line
y = mx + a/m and y = -x/m – am
are tangents to the parabola and they intersect at right angles. Their point of intersection satisfies the equation
x(m + 1/m) = -a(m + 1/m)
Hence, the locus of the point of intersection is the line x −a which is the directrix.