The point of intersection of the tangents at t1 = t and t2 = 3t to the

1.	The point of intersection of the tangents at t1 = t and t2 = 3t to the parabola y2 = 8x is …(a) (6t2, 8t) (b) (8t, 6t2) (c) (t2, 4t) (d) (4t, t2)
Answer» (a) (6t², 8t) Point of intersection of the tangents at t₁ and t₂ to y² = 4ax is [at₁t₂, a(t₁+ t₂)] Here, t₁ = t, t₂ = 3t, a = \(\frac{8}{4}\) = 2 So a t₁t₂ = 2(t) (3t) = 6t² a(t₁ + t₂) = 2(t + 3t) = 8t ∴ Point = (6t², 8t²)

The point of intersection of the tangents at t1 = t and t2 = 3t to the parabola y2 = 8x is …(a) (6t2, 8t) (b) (8t, 6t2) (c) (t2, 4t) (d) (4t, t2)

Answer»

(a) (6t², 8t)

Point of intersection of the tangents at t₁ and t₂ to

y² = 4ax is [at₁t₂, a(t₁+ t₂)]

Here, t₁ = t, t₂ = 3t,

a = \(\frac{8}{4}\) = 2

So a t₁t₂ = 2(t) (3t) = 6t²

a(t₁ + t₂) = 2(t + 3t) = 8t

∴ Point = (6t², 8t²)