Parabola
A chord of the parabola y^2 = 8x passes through its focus and is perpendicular to the axis; what is the total length of this latus rectum chord?
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- parabola
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
8
The latus rectum of a parabola is the focal chord perpendicular to the axis, and for y^2 = 4ax its length equals 4a, a result that follows directly from substituting the focus abscissa. Matching y^2 = 8x to y^2 = 4ax gives 4a = 8, so a = 2 and the latus rectum length is 4a = 8. Concretely, at the focus x = a = 2 the equation gives y^2 = 8(2) = 16, so y = ±4, and the chord runs from (2, 4) to (2, -4), a length of 8. Option 4 mistakes the semi-latus rectum 2a for the full chord. Option 16 squares incorrectly or doubles 4a. Option 2 reports a instead of 4a. This is the standard JEE Advanced latus rectum derivation. Plausibility check: the endpoints (2, ±4) both satisfy y^2 = 8x since 16 = 16, and their vertical separation is exactly 8, matching 4a and confirming the geometry.
This medium difficulty mathematics question is from the chapter coordinate geometry, covering the topic of parabola. It appeared in the 2025 exam.
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