Let the focus ( S ) of a parabola divides its one of the focal chords P Q in the ratio 2 : 1 . If the tangent at Q cuts the directrix at R such that R Q = 6 , then the distance (in units) of the focus from the tangent at P is

Step-by-step solution

Let, the foot of the perpendicular from the focus on the tangent P R is A which lies on the tangent at the vertex. Also, ∠ P R Q = 9 0 o Now, in Δ P R Q & Δ P A S , ∠ P is common & ∠ R = ∠ A Then, Δ P R Q is similar to Δ P A S ⇒ P S P Q = A S R Q = 2 3 ⇒ A S = 2 3 × 6 = 4 ⇒ The distance of the focus from the tangent at P = 4 units