Question 673487

the line that passes through ({{{1}}},{{{1}}}) and through the center ({{{h}}},{{{k}}}) of the circle {{{(x-2)^2+ (y-4)^2=20}}}

recall the standard form equation of a circle formula {{{(x-h)^2+(y-k)^2=r^2}}}

where {{{h}}} and {{{k}}} are the {{{x}}} and {{{y}}} coordinates of the center of the circle 

and the center of the circle will be second point the line that passes through

as you can see from {{{(x-2)^2+ (y-4)^2=20}}}, ({{{h}}},{{{k}}})=({{{2}}},{{{4}}})  and {{{r=sqrt(20)=4.47}}}

now we can find the equation of a line that passes through ({{{1}}},{{{1}}}) and ({{{2}}},{{{4}}})


*[invoke find_equation_of_line 1, 1, 2, 4]


{{{drawing(600,600,-10,10,-10,10,grid(1),
         blue( circle( 2, 4, 4.47, 1 )),circle(2,4,0.2),circle(1,1,0.2),graph(600,600,-10,10,-10,10,3x-2))}}}