Length of chord PQ is 7a, 2a, 5a, 3a?

Let P(at²,2at), Q(at², -2at) as PQ is focal chord. Point of intersection of tangents at P and Q (-a, a(t + 1/t)). As point of intersection lies on y = 2x + a ⇒ a(t + 1/t) = -2a + at ⇒ t + 1/t = -2 + t ⇒ 1/t = -2 which is not possible. Let P(at1², 2at1), Q(at2², 2at2). Length of chord PQ = a(t1 + t2)² If PQ is focal chord then t1t2 = -1. Length of focal chord = a(t1 - t2)² = a(t1 + 1/t1)² Let PQ be a focal chord. Then the coordinates of P and Q are (at², 2at) and (at², -2at) respectively. The equation of the chord PQ is y = 0. Length of the chord PQ is 4at. If the chord PQ subtends a right angle at the vertex, then length of chord PQ is 4a. If the equation of the chord is y = mx + a/m, then the length is a(1 + m²)^(3/2) / m². If the chord is focal chord then the length is a(t + 1/t)² = 5a.