Parabola
The standard equation of a parabola with vertex at origin and focus on positive x-axis is
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- parabola
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
y² = 4ax
- Locus Definition: A parabola is the set of points equidistant from a focus (a,0) and a directrix x=−a.
- Derivation: For a point (x,y), (x−a)2+y2=∣x+a∣.
- Simplification: (x−a)2+y2=(x+a)2⟹x2−2ax+a2+y2=x2+2ax+a2.
- Result: y2=4ax. This parabola opens to the right and is symmetric about the x-axis.
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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