The equation of a circle is 

(x2 - 4x + 3) + (y2 - 6y + 8) = 0

Which of the following statements are correct?

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

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

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

Select the answer using the code given below.

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. I and II only
  2. II and III only
  3. I and III only
  4. I, II and III

Answer (Detailed Solution Below)

Option 1 : I and II only
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Detailed Solution

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Explanation:

Given

Equation of circle is  

(x2 - 4x + 3) + (y2 - 6y + 8) = 0

⇒ (x – 3) (x – 1) + (y – 4) (y – 2)= 0

So the possible ends of the diameters are (3, 4), (3, 2), (1, 4) and (1, 2). 

Also, Radius = √2 

center = (2,3)

So the required pair of ends of diameters are (I) (1, 2) and (3, 4) and (II) (1, 4) and (3, 2).

∴ Option (a) is correct.

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