A square is inscribed in the circle x2 + y2 andndash; 2x + 4y + 3 = 0. Its sides are parallel to the coordinate axes. The one vertex of the square is (1980)a)(1 + , andndash; 2)b)(1 andndash; , andndash; 2)c)(1, andndash; 2 + )d)none of theseCorrect answer is option 'D'. Can you explain this answer?

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A square is inscribed in the circle x²+ y²– 2x + 4y + 3 = 0. Its sides are parallel to the coordinate axes. The one vertex of the square is (1980)

a)
(1 + , – 2)
b)
(1 – , – 2)
c)
(1, – 2 + )
d)
none of these

Correct answer is option 'D'. Can you explain this answer?

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A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. I...

The given circle is x² + y² – 2x + 4y + 3 = 0. Centre (1, – 2). Lines through centre (1, – 2) and parallel to axes are x = 1 and y = – 2.

Let the side of square be 2k.
Then sides of square are x = 1 – k and x = 1 + k and y = – 2 – k and y = – 2 + k
∴ Co-ordinates of P, Q, R, S are (1 + k, – 2 + k), (1 – k, – 2 + k), (1 – k, – 2 – k), (1 + k, – 2 – k) respectively.
Also P (1 + k, – 2 + k) lies on circle
∴ (1 + k)² + (– 2 + k)² – 2 (1 + k) + 4 (–2 + k) + 3 = 0 ⇒ 2k² = 2
⇒ k = 1 or – 1 If k = 1, P (2, – 1), Q (0, – 1), R (0, – 3), S (2, – 3)
If k = – 1, P (0, – 3), Q (2, – 3), R (2, – 1), S(0, – 1)

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A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. Its sides are parallel to the coordinate axes. The one vertex of the square is (1980)a)(1 + , – 2)b)(1 – , – 2)c)(1, – 2 + )d)none of theseCorrect answer is option 'D'. Can you explain this answer?

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