Menu Close

If-p-x-1-x-2-x-i-and-q-y-1-y-2-y-i-form-two-infinite-arithmetic-sequences-with-common-difference-a-and-b-respectively-then-find-the-locus-of-the-point-where-1-n-




Question Number 61274 by alphaprime last updated on 31/May/19
If p , x_1 ,x_2 ,...x_i  and q,y_1 ,y_2 ,...y_i  form two   infinite arithmetic sequences with common   difference  a and b respectively ,  then find the locus of the point ( α , β )   where α = (1/n) Σ_(i=1) ^n x_i  and β= (1/n) Σ_(i=1) ^n y_(i .)
Ifp,x1,x2,xiandq,y1,y2,yiformtwoinfinitearithmeticsequenceswithcommondifferenceaandbrespectively,thenfindthelocusofthepoint(α,β)whereα=1ni=1nxiandβ=1ni=1nyi.
Answered by tanmay last updated on 31/May/19
α=((x_1 +x_2 +x_3 +...+x_n )/n)  α=(((p+a)+(p+2a)+...+(p+na))/n)  α=((np+a[((n(n+1))/2)])/n)  α=p+((a(n+1))/2)  β=q+((b(n+1))/2)  ((α−p)/(a/2))=((β−q)/(b/2))  so locus...  b(x−p)=a(y−q)  bx−ay+aq−bp=0  ean of straight line→locus st line...
α=x1+x2+x3++xnnα=(p+a)+(p+2a)++(p+na)nα=np+a[n(n+1)2]nα=p+a(n+1)2β=q+b(n+1)2αpa2=βqb2solocusb(xp)=a(yq)bxay+aqbp=0eanofstraightlinelocusstline
Commented by bhanukumarb2@gmail.com last updated on 31/May/19
sir congrates for goiit approval pleasd  share ur approch their also
sircongratesforgoiitapprovalpleasdshareurapprochtheiralso
Commented by bhanukumarb2@gmail.com last updated on 31/May/19
tanmay sir
tanmaysir
Commented by tanmay last updated on 31/May/19
thank you sir...let me check in goiit
thankyousirletmecheckingoiit

Leave a Reply

Your email address will not be published. Required fields are marked *