Part of CG-03 — Parabola

Intersection of Tangents

by Notetube Official64 words9 views

Tangents at parameters t1 and t2 on y2y^2 = 4ax meet at the point (at1t2, a(t1+t2)). This is a key result: the x-coordinate is a times the product and the y-coordinate is a times the sum. For a focal chord (t1t2=-1), the tangents meet at (-a, a(t1+t2)), which lies on the directrix x=-a. The tangents at the ends of a focal chord are perpendicular.

Like these notes? Save your own copy and start studying with NoteTube's AI tools.

Sign up free to clone these notes