Question 1008367


for what value of k does circle {{{(x+2k)^2+(y-3k)^2=10}}} passes through point ({{{1}}},{{{0}}}) 

substitute {{{1}}} for {{{x}}} and {{{0}}} for {{{y}}}

 {{{(1+2k)^2+(0-3k)^2=10}}}

 {{{1+4k+4k^2+9k^2=10}}}

{{{13k^2+4k+1-10=0}}}

{{{13k^2+4k-9=0}}}

{{{13k^2+13k-9k-9=0}}}

{{{(13k^2+13k)-(9k+9)=0}}}

{{{13k(k+1)-9(k+1)=0}}}

{{{(13k-9)(k+1)=0}}}

solutions:

{{{13k-9=0}}} => {{{13k=9}}} => {{{k=9/13}}}
{{{k+1=0}}} => {{{k=-1}}}