The equation of the circle having the lines $y^2 - 2y + 4x - 2xy = 0$ as its normals $\&$ passing through the point $(2 , 1)$ is :

  • A

    $x^2 + y^2 - 2x - 4y + 3 = 0$

  • B

    $x^2 + y^2 - 2x + 4y - 5 = 0$

  • C

    $x^2 + y^2 + 2x + 4y - 13 = 0$

  • D

    none

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  • [IIT 1975]

The equation of circle which touches the axes of coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is ${x^2} + {y^2} - 2cx - 2cy + {c^2} = 0$, where $c$ is