The correct option is
A The idea that focuses on the topic by giving direction to the composition.
The correct answer is Option A
The question is on the definition of the controlling idea of a paragraph.
The controlling idea contains your opinion on the topic. It shows what direction you are going to take in writing about the topic. It helps the reader to understand your purpose for writing the paragraph.
It is not a particular line in the paragraph. Hence Option D is incorrect.
The conclusion of a paragraph ends the paragraph by summarizing the ideas expressed in it. Option C is therefore not the correct answer.
Option B is also incorrect because actually the main subject matter covered in the paragraph depends on the controlling idea. The main subject is in accordance with the direction of the composition of paragraph.
So, according to the definition mentioned above, Option A is the correct answer.
The controlling idea of a paragraph is the idea that focuses on the topic by giving direction to the composition.