Find the equation of the circle having centre in the first quadrant, touching the x-axis, having a common tangent y= - Maths - Conic Sections

Question

Find the equation of the circle having centre in the first
quadrant, touching the x-axis, having a common tangent y= (sqrt3) x
+ 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

Mayank Jha · Accepted Answer

Dear student,

Your question is wrong
We haveC:x2+y2+4x+4y+4=0Centre is -2,2 and radius is -22+-22-4=4+4-4=2If y=3x+4 touches C then perpendicular from centre to line must beequal to radius of circle
y=3x+4 ⇒3x-y+4=0Length of perpendicular=3×-2-2+432+-12=23+22=23+12=3+1 which is not equal to radius of cirlcle
 Hence line cannot be tangentto cirlce
Hence information given in question is incorrect

Regards

Find the equation of the circle having centre in the first quadrant, touching the x-axis, having a common tangent y= (sqrt3) x + 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.