Find the locus of the centre of the circle touching the line `x+2y=0a n dx=2y=0.`

Options

A. xy=0
B. x=0
C. y=0
D. none of these

Answer

A

Explanation

Let (h, k) be the centre and r be the radius of the circle. As it touches the lines x+2y=0 and x-2y=0.
`:. |(h+2k)/(sqrt(5))|=(h-2k)/(sqrt(5))|=`Radius
`rArrh+2k=pm(h-2k)`
`rArr k=0 or, h=0`
`rArr` Locus of (h, k) is x=0 or, y=0
Hence, the locus of (h, k) is xy=0.