Parabola
For the parabola described by y^2 = 12x, determine the coordinates of its focus together with the equation of its directrix line.
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- parabola
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
Focus(3,0),directrixx=−3
A right-opening parabola in standard form y^2 = 4ax has its focus at (a, 0) and directrix x = -a, so the entire geometry is fixed by reading off 4a. Comparing y^2 = 12x with y^2 = 4ax gives 4a = 12, hence a = 3. The focus is therefore (3, 0) and the directrix is the vertical line x = -3. Option Focus (0, 3) wrongly treats the parabola as opening upward, which would require x^2 = 4ay. Option Focus (6, 0) uses a = 6 by mistaking 12 for 2a. Option directrix x = 3 puts the directrix on the focus side, contradicting the defining reflection symmetry. This is the textbook JEE Advanced standard-form parabola identification. Plausibility check: every point on the curve is equidistant from (3, 0) and the line x = -3; testing the vertex (0,0) gives distance 3 to each, confirming the focus-directrix pair is consistent.
This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of parabola. It appeared in the 2025 exam.
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