Show-that-any-circle-with-centre-2-3-cannot-pass-through-more-than-one-lattice-point-Lattice-points-are-points-in-cartesian-plane-whose-abscissa-and-ordinate-both-are-integers- Tinku Tara June 4, 2023 Algebra 0 Comments FacebookTweetPin Question Number 13394 by Tinkutara last updated on 19/May/17 Showthatanycirclewithcentre(2,3)cannotpassthroughmorethanonelatticepoint.[Latticepointsarepointsincartesianplane,whoseabscissaandordinatebothareintegers.] Answered by mrW1 last updated on 20/May/17 circlethroughlatticepoint(i,j)withi,jϵZ(i−2)2+(j−3)2=r2foranyotherpoint(x,y)onthiscircle,(x−2)2+(y−3)2=r2=(i−2)2+(j−3)2(x−2)2−(i−2)2+(y−3)2−(j−3)2=0(x+i−22)(x−i)+(y+j−23)(y−j)=0(x+i)(x−i)−2(x−i)2+(y+j)(y−j)−2(y−j)3=0x2−i2+y2−j2=2(x−i)2+2(y−j)3case1:ifx≠iandy=jx2−i2=2(x−i)2⇒2=x+i2=integer2butthisisfalse,since2isirrational.case2:ifx=iandy≠jy2−j2=2(y−j)3⇒3=y+j2=integer2butthisisfalse,since3isirrational.case3:ifx≠iandy≠j(x2−i2+y2−j2)2=8(x−i)2+12(y−j)2+8(x−i)(y−j)6⇒6=(x2−i2+y2−j2)2−8(x−i)2−12(y−j)28(x−i)(y−j)⇒6=integerintegerbutthisisfalse,since6isirrational.⇒xandycannotbeintegerboth,exceptx=iandy=j. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: If-C-226k-find-the-least-integal-value-of-k-that-will-make-C-a-perfect-square-Next Next post: if-x-1-x-a-find-x-n-1-x-n- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.