Question

^{_{​​​​​​A rod AB of length 4 units moves horizontally with its left end A always on the circle} ​​​}x _{​​​​​​}²+y²-4x-18y-29=0 then the locus of the circle is

Answer 1

We have
x² + y²−4x−18y−29=0
As rod is of length of 4,and end A is on above
circle and it moves horizontally,simiply replace x→x−4
to get locus of the circle.
(x−4)²+ y²−4(x−4)−18y−29=0
⇒
x²+16−8x+y²−4x+16−18y−29=0
⇒
x²+y²−12x−18y+3=0 => ans


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