Multiple choice general knowledge math & puzzles

The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y - 3 = 0 is

  1. (-3,-4)

  2. (-3,4)

  3. (3,4)

  4. (-4,-1)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The circle x² + y² + 2x + 4y - 3 = 0 has center at (-1, -2) and radius 3. Point P(1,0) is on the circle. The diametrically opposite point Q is found by: Q = 2*center - P = 2*(-1,-2) - (1,0) = (-2,-4) - (1,0) = (-3,-4). This places Q opposite to P through the center, at distance 6 from P (the diameter).

AI explanation

Rewriting the circle equation x^2+y^2+2x+4y-3=0 in center-radius form gives center (-1,-2). For any point on a circle, the point diametrically opposite it is found by reflecting through the center: (2*(-1)-1, 2*(-2)-0) = (-3,-4). Checking P(1,0) confirms it lies on the circle, so its diametric opposite is indeed (-3,-4).

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