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NDA 2 2024 Maths, question 59

Topic: Analytical geometry

Q59

The equation of a circle is

(x2−4x+3)+(y2−6y+8)=0(x^{2}-4x+3)+(y^{2}-6y+8)=0

Which of the following statements are correct?

I. The end points of a diameter of the circle are at (1,2)(1,2) and (3,4)(3,4).

II. The end points of a diameter of the circle are at (1,4)(1,4) and (3,2)(3,2).

III. The end points of a diameter of the circle are at (2,4)(2,4) and (4,2)(4,2).

Select the answer using the code given below.

  1. (a) I and II onlyCorrect answer
  2. (b) II and III only
  3. (c) I and III only
  4. (d) I, II and III

Solution.

Answer: (a) I and II only

  1. Complete squares to obtain (x−2)²+(y−3)²=2, with centre (2,3).
  2. Both pairs I and II have this midpoint, and each endpoint is at distance √2 from it.
  3. Pair III has midpoint (3,3), so it is not a diameter.
  4. I and II only are correct.