JEE Main 2022 · 27 July · evening · Single correct · +4 / −1
If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x+y=a, is 16, then |a| is equal to :
- (a) 2 √2
- (b) 2 √3
- (c) 4 √2
- (d) 4
Answer and solution
Answer (c) 4 √2
Solution
Maths sir · 3 steps
The focus-to-vertex distance is just the gap from the focus to the tangent at the vertex.
- What A means. In any parabola, the distance from the focus to the vertex is A, and the latus rectum is 4A. The tangent at the vertex is perpendicular to the axis, so A is the perpendicular distance from the focus to that tangent.
A = (|a + a - a|)/√(1² + 1²) = |a|/√2
- Use the latus rectum. 4A = 16 gives 4 × |a|/√2 = 16, so 2√2 |a| = 16.
- So. |a| = 16/2√2 = 8/√2 = 4√2, which is option (c).
The idea to keep. For a tilted parabola, do not rotate axes. Focus to tangent at vertex is A, and focus to directrix is 2A. One distance formula, then latus rectum = 4A.
Answer from the NTA final answer key. Solution by PrepWiser.