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Equation of a circle touching the y-axis...

Equation of a circle touching the y-axis
at origin is `x^2+y^2-2ax=0`.Find the
DE of all such circles.

Answer

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a)Equation of family of circles touching the y -axis at origin is x^2+y^2-2 a x=0 Find the differential equation of all circles b) Solve the differential equation (1+x^2) (dy)/(dx)+y=tan ^-1x

Form the DE of the family of circles touching the x-axix at origin.

Knowledge Check

  • The equation of the circle which touches the lines x=0, y=0 and 4x + 3y =12 is

    A
    `x^(2) +y^(2) - 2x - 2y - 1 =0`
    B
    `x^(2) - y^(2) - 2x - 2y + 3 =0`
    C
    `x^(2) +y^(2) - 2x - 2y + 2 =0`
    D
    `x^(2) + y^(2) - 2x - 2y + 1=0`

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