MP Board · Class 11 · Mathematics · Conic SectionsWhich of the following represents a parabola?
Step-by-Step Solution
A parabola is a conic section with an eccentricity $e = 1$. Mathematically, in the general equation of second degree, $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$, a parabola is formed when $B^2 - 4AC = 0$ (and it does not degenerate). Among the options, $y^2 = 4ax$ is the standard equation of a parabola.
Detailed Options Breakdown
Option : $y^2 = 4ax$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
Option 2: $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
Option 3: $x^2 + y^2 = r^2$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
💡 Study Guide: This question tests core syllabus concepts from Conic Sections. For formulas, key summaries, and mock exam reference guides, read the full Conic Sections Revision Notes.