NCERT · Class 11 · Mathematics · Conic SectionsThe equation of the circle with centre $(0, 2)$ and radius $2$ is:
Step-by-Step Solution
The standard equation of a circle with centre $(h, k)$ and radius $r$ is given by $(x - h)^2 + (y - k)^2 = r^2$. Substituting $h = 0$, $k = 2$, and $r = 2$, we get $(x - 0)^2 + (y - 2)^2 = 2^2$, which simplifies to $x^2 + y^2 - 4y = 0$.
Detailed Options Breakdown
Option : $x^2 + y^2 - 4y = 0$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $x^2 + y^2 + 4y = 0$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
Option 2: $x^2 + y^2 - 4x = 0$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Conic Sections.
Option 3: $x^2 + y^2 - 2y = 0$
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.