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MHT CET20239 May 2023Evening ShiftMathematicsCircleActual

18. The sides of a rectangle are given by the equations x=-2, x=4, y=-2 and y=5 Then the equation of the circle, whose centre is the point of intersection of the diagonals, lying within the rectangle and touching only two opposite sides, is

Options

  1. Ax^2+y^2+2 x+3 y+9=0
  2. Bx^2+y^2-2 x+3 y+9=0
  3. Cx^2+y^2+2 x-3 y-9=0
  4. Dx^2+y^2-2 x-3 y-9=0

Correct answer

D. x^2+y^2-2 x-3 y-9=0

Step-by-step solution

The given equations of the sides are x=-2 , x=4, y=-2, y=5 According to the given condition, centre of the required circle is P . The co-ordinates of P are (1, 3 2 ) . As circle touches only 2 opposite sides, its radius is either 3.5 units or 3 units. Equation of the required circle is aligned & x^2+y^2-2 x-3 y- 23 4 =0 or & x^2+y^2-2 x-3 y-9=0 aligned Option (D) is correct.

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