Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations exist, so the description carries the full burden, and it does disclose the return payload (standard equation, foci, eccentricity, directrix, asymptotes). It does not say how irrelevant parameters are handled (e.g., supplying p for a circle) or anything about failure modes, so it stops short of full transparency.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the purpose, then inputs, then returns, then intended use – every clause earns its place and nothing is padded. Slightly dense inline enumeration but efficient overall.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a pure computation/rendering tool with no annotations and no output schema, the description covers purpose, inputs and returned values, which is most of what an agent needs. Gaps remain around parameter applicability per conic type, the locale-driven rendering side effect, and error behavior.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so all five parameters including the type enum and locale are already documented in the schema. The description restates a/b/p semantics and adds the y²=2px convention, which is consistent but largely redundant; the locale parameter is not mentioned at all.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource ('Plot a conic section') and enumerates the four supported types plus the returned quantities. It is distinguishable from nearby math/graphing siblings (function_grapher, geometry-lab, trig-lab) by topic and by the conic-specific outputs, though it does not name a sibling to differentiate against.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

'Use for high-school conic-section teaching' implies the intended context but gives no when-not conditions, prerequisites, or alternatives (e.g., vs function-grapher for arbitrary curves). Usage is implied rather than specified.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.