Equation of circles touching x-axis at the origin and the line 4x−3y+24=0 are
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a
x2+y2−6y=0,x2+y2+24y=0
b
x2+y2+2y=0,x2+y2−18y=0
c
x2+y2+18x=0,x2+y2−8x=0
d
x2+y2+4x=0,x2+y2−16x=0
answer is A.
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Detailed Solution
Given line is 4x−3y+24=0 Since equation of circles touching x-axis at the origin thenCentre = (0, r)radius, r=d =The perpendicular distance from centre to the line⇒r=|0−3r+24|5∴r=12, r=3∴ The equation of the circle is (x−h)2+(y−k)2=r2(x−0)2+(y−3)2=9 or(x−0)2+(y+12)2=144⇒x2+y2−6y=0,x2+y2+24y=0