A (x1,y1) is an external pt. on the circle x2+y2=a2.a variable straight line is drawn through A cutting the circle at B n C.if P is a pt. on BC such that AB,AP,AC r in A.P.,then locus of p is???
ans.x(x-x1)+y(y-y1)=0
-
UP 0 DOWN 0 0 1
1 Answers
1this is easy ..
we have from the givn AP
AP-AB=AC-AP thus
BP=PC thus P is the midpoint ..
as P is the mid point OP is perpendicular to AP
let P be h,k
we have equation of line =y(h-x1) - x(k-y1) +kx1 -hy1=0
distance of this line from O=OP =h2 + k2
further this is also = kx1-hy1/√(h-x1)2 + (k-y1)2
thus the result
