1.

Two tangents are drawn from any point P on a given line L=0 to a given circle S=0, if these tangents touch the circle at point A and B, then locus of the circumcentre the DeltaPAB will be

Answer»

A pair of straight lines
A circle touching the given line `L=0`
A circle touching the given circle `S=0`
A line parallel to given line `L=0`

Solution :
The circumcirle of `DeltaPAB` PASSES through C with PC as its diameter. Therefore centre of this circle `(C_(1))` will be MID pt of PC.
Let `L=ax+by+c=0`
`P(x_(1).y_(1)) & C(p,q)`
`C_(1)(H,k)`
`h=(x_(1)+p)/(2)`
`k=(y_(1)+q)/(2)`
`p(x_(1),y_(1))` passes through `L=0`
`impliesax_(1)+by_(1)+c=0`
or `a(2h-p)+b(2k-q)+c=0`
or `2ah+2bk-ap-bq+c=0`
Locus of `(h,k)` is `ax+by=(ap+bq+c)/(2)`
`implies` A line parallel to `L=0`


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