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find the equation of the circle having the centre in the first quadrant touching the x-axis having a common tangent y equal to root 3 X + c with the circle X square + y square + 4 x + 4 y + 4 = 20 such that distance between the two circles along the x axis is 3 units also deduce the value of c

find the equation of the circle having the centre in the first quadrant touching the x-axis having a common tangent y equal to root 3 X + c with the circle X square + y square + 4 x + 4 y + 4 = 20 such that distance between the two circles along the x axis is 3 units also deduce the value of c

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Grade:11

1 Answers

Arun
25763 Points
2 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 and put in equation 1

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