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MHT CET202521 Apr 2025Morning ShiftMathematicsCircleActual

The minimum distance and maximum distance of the point P (2,-7) from the circle x^2+y^2-14 x-10 y-151=0 are respectively _______ units

Options

  1. A2,28
  2. B5,25
  3. C6,24
  4. D3,27

Correct answer

A. 2,28

Step-by-step solution

The minimum and maximum distances from point P(x₁, y₁) to a circle are determined using its center C(h, k) and radius R . The given circle equation is x^2 + y^2 - 14x - 10y - 151 = 0 . By rewriting in standard form, the center is C(7, 5) and radius R = (-7)^2 + (-5)^2 - (-151) = 49 + 25 + 151 = 15 units. For point P(2, -7) , the distance to the center is d = (7 - 2)^2 + (5 - (-7))^2 = 25 + 144 = 13 units. The minimum distance is |d - R| = |13 - 15| = 2 units, and the maximum is d + R = 13 + 15 = 28 units. Among the

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