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COMEDK20269 May 2026Evening ShiftMathematicsStraight LinesActual

Let point Q be the image of point P(2, -1) in the line 3x + 5 = 4y . Find the area of the circle that has the segment PQ as the diameter.

Options

  1. A1.96
  2. B3
  3. C9
  4. D36

Correct answer

C. 9

Step-by-step solution

The equation of the given line is 3x - 4y + 5 = 0 . Since Q is the image of P(2, -1) in the given line, the line acts as the perpendicular bisector of the segment PQ . The distance from point P to the line is equal to half the length of PQ , which is the radius r of the circle having PQ as its diameter. r = |3(2) - 4(-1) + 5| 3^2 + (-4)^2 r = |6 + 4 + 5| 5 = 15 5 = 3 The area of the circle is r^2 = (3)^2 = 9 . Answer: 9

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