SECTION 3 (Maximum Marks: 12)

• This section contains TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions.

• Each question has FOUR options. ONLY ONE of these four options corresponds to the correct answer.

• For each question, choose the option corresponding to the correct answer.

• Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +3 If ONLY the correct option is chosen.

Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).

Negative Marks : -1 In all other cases.

PARAGRAPH "X"

Let S be the circle in the x-y plane defined by the equation x 2 + y 2 = 4.

(There are two questions based on PARAGRAPH "X", the question given below is one of them)

(i) Let E 1 E 2 and F 1 F 2 be the chords of S passing through the point P 0 (1, 1) and parallel to the x-axis and the y-axis, respectively. Let GiG 2 be the chord of S passing through P 0 and having slope -1. Let the tangents to S at E 1 and E 2 meet at E 3 , the tangents to S at F 1 and F 2 meet at F 3 , and the tangents to S at G 1 and G 2 meet at G 3 . Then, the points E 3 , F 3 , and G 3 lie on the curve