3 Sirkels op die y-as

3 Sirkels op die y-as

by Simeon Oberholzer -
Number of replies: 1


In reply to Simeon Oberholzer

Re: 3 Sirkels op die y-as

by Marna Zuhlsdorff -

Hi Simeon

Awesome vraag - baie dankie!

Ek het sommer 'n video daaroor gemaak - click hier

1.1)

Bepaal die middelpunt en radius uit onderste sirkel (vierkantsvoltooiing)

table row cell x squared plus y squared plus 8 y equals 65 end cell row cell x squared plus y squared plus 8 y plus open parentheses 8 over 2 close parentheses squared equals 65 plus open parentheses 8 over 2 close parentheses squared end cell row cell x squared plus open square brackets y plus 8 over 2 close square brackets squared equals 81 end cell row cell x squared plus open parentheses y plus 4 close parentheses squared equals 81 end cell row cell middelpunt space van space straight O equals open parentheses 0 semicolon minus 4 close parentheses end cell row cell r a d i u s equals square root of 81 equals 9 end cell end table

table attributes columnalign left end attributes row cell U space is space die space onderste space punt space van space straight O comma space daarom space left parenthesis middelpunt space minus space radius right parenthesis end cell row cell bold italic U open parentheses 0 semicolon minus 4 minus 9 close parentheses equals open parentheses 0 semicolon minus 13 close parentheses end cell row cell S space is space die space boonste space punt space van space straight O comma space daarom space left parenthesis middelpunt space plus space radius right parenthesis end cell row cell bold italic S open parentheses 0 semicolon minus 4 plus 9 close parentheses equals open parentheses 0 semicolon 5 close parentheses end cell end table


table attributes columnalign left end attributes row cell Bepaal space bo space en space onder space punte space van space die space middelste space sirkel space left parenthesis straight r squared equals 81 right parenthesis end cell row cell straight x squared plus open parentheses y minus 8 close parentheses squared equals 81 end cell row cell m i d d e l p u n t space van space straight M open parentheses 0 semicolon 8 close parentheses space en space radius space is space 9 end cell row cell T space is space die space onderste space punt space van space straight M comma space daarom space left parenthesis middelpunt space minus space radius right parenthesis end cell row cell bold italic T open parentheses 0 semicolon 8 minus 9 close parentheses equals open parentheses 0 semicolon minus 1 close parentheses end cell row cell Q space is space die space boonste space punt space van space straight M comma space daarom space left parenthesis middelpunt space plusr space adius right parenthesis end cell row cell bold italic Q open parentheses 0 semicolon 8 plus 9 close parentheses equals open parentheses 0 semicolon 17 close parentheses end cell end table


table attributes columnalign left end attributes row cell Bepaal space bo space en space onderpunte space van space die space boonste space sirkel space 0 left parenthesis straight r squared equals 81 right parenthesis end cell row cell straight x squared plus open parentheses y minus b close parentheses squared equals 81 end cell row cell m i d d e l p u n t space van space straight B open parentheses 0 semicolon b close parentheses space en space radius space is space 9 end cell row cell bold italic R space is space die space onderste space punt space van space straight B comma space daarom space left parenthesis middelpunt space minus space radius right parenthesis end cell row cell R open parentheses 0 semicolon b minus 9 close parentheses end cell row cell bold italic D space is space die space boonste space punt space van space straight B comma space daarom space left parenthesis middelpunt space plus space radius right parenthesis end cell row cell D open parentheses 0 semicolon b plus 9 close parentheses end cell end table


table row cell Q R equals S T end cell row cell Q subscript y minus R subscript y equals S subscript y minus T subscript y end cell row cell 17 minus open parentheses b plus 9 close parentheses equals 5 minus open parentheses negative 1 close parentheses end cell row cell 17 minus b minus 9 equals 5 plus 1 end cell row cell 26 minus b equals 6 end cell row cell 26 minus 6 equals b end cell row cell b equals 20 end cell end table

vergelyking space van space boonste space sirkel space straight B colon bold x to the power of bold 2 bold plus begin bold style left parenthesis y minus 20 right parenthesis end style to the power of bold 2 bold equals bold 81


1.2)

table attributes columnalign left end attributes row cell uit 1.1 right parenthesis end cell row cell Q open parentheses 0 semicolon 8 plus 9 close parentheses equals open parentheses 0 semicolon 17 close parentheses end cell row cell R open parentheses 0 semicolon b minus 9 close parentheses equals R open parentheses 0 semicolon 20 minus 9 close parentheses equals R open parentheses 0 semicolon 11 close parentheses end cell row blank row cell Q R equals Q subscript y minus R subscript y equals 17 minus 11 equals bold 6 bold eennhede end cell end table