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Find the equation of the circle having center in the first quadrant, touching the x – axis, having a common tangent y = √3x +4 with the circle x^2 + y^2 + 4x + 4y + 4 = 0 such that the distance between the two circles along the x – axis is 3 units

Find the equation of the circle having center in the first quadrant, touching the x – axis, having a common tangent y = √3x +4 with the circle x^2 + y^2 + 4x + 4y + 4 = 0 such that the distance between the two circles along the x – axis is 3 units

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
 
Let the equation of the circle having center in the first quadrant,
be
x^2 + y^2 + 2gx + 2fy + c = 0......................(1)
 touching the x – axis, .i.e y = 0 put it in eqn. (1),
and
and apply the formulae of distance b/e their centeres for second eqn.
 
Put y = root3x + 4 in x^2 + y^2 + 4x + 4y + 4 = 0 
and get the roots of x andd put in eqn. (1)
and solve for g, f and c

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