JEE Main 2022 · 28 June · evening · Single correct · +4 / −1

If vertex of a parabola is (2, -1) and the equation of its directrix is 4x - 3y = 21, then the length of its latus rectum is :

  1. (a) 2
  2. (b) 8
  3. (c) 12
  4. (d) 16
Answer and solution

Answer (b) 8

Solution

Maths sir · 3 steps

The vertex sits exactly a away from the directrix, so one distance formula gives you a, and then 4a.

  1. What a means. For a parabola, the vertex is midway between the focus and the directrix. So the perpendicular distance from the vertex to the directrix is a, and the latus rectum is 4a.

    a = (|4(2) - 3(-1) - 21|)/√(4² + 3²) = (|8 + 3 - 21|)/5 = 10/5 = 2

  2. Latus rectum. Length of latus rectum = 4a = 4 × 2 = 8.
  3. So. The latus rectum is 8, which is option (b).

The idea to keep. Vertex to directrix (or vertex to focus) is a. Focus to directrix is 2a. Latus rectum is 4a. Find any one of these distances and the rest follow, even for a tilted parabola.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Parabola

Asked about 110 times in JEE Main since 2020. This question is from 2022.