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AP EAMCET20225 Jul 2022Morning ShiftMathematicsCircleActual

A circle is such that (x-2) +(y-2) =1 touches it for all values of . Then, the circle is

Options

  1. Ax^2+y^2-4 x-4 y+7=0
  2. Bx^2+y^2+4 x+4 y+7=0
  3. Cx^2+y^2-4 x-4 y-7=0
  4. Dx^2+y^2+4 x+4 y-7=0

Correct answer

A. x^2+y^2-4 x-4 y+7=0

Step-by-step solution

Since, the line (x-2) +(y-2) =1 touches a circle. So it is a tangent equation to a circle. Equation of tangent to a circle at (x₁, y₁ ) is (x-h) x₁+(y-k) y₁=a^2 to a circle (x-h)^2+(y-k)^2=a^2 Then, after comparing aligned & x-h=x-2 y-k=y-2 and a^2=1 & x₁= , y₁= aligned Required equation of circle (x-2)^2+(y-2)^2=1 x^2+y^2-4 x-4 y+7=0

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