Question 744884
{{{x^2+y^2-8x+14y+65=36}}}.......write {{{65}}} as {{{16+49}}}

{{{x^2+y^2-8x+14y+16+49=36}}}.....group

{{{(x^2-8x+16)+(y^2+14y+49)=36}}}

{{{(x-4)^2+(y+7)^2=36}}}

so, {{{h=4}}}, {{{k=-7}}}, {{{r=6}}}

the center is at: ({{{4}}},{{{-7}}})

radius: {{{r=6}}}

{{{x-intercepts}}} occur when {{{y = 0}}}

{{{(x-4)^2+(0+7)^2=36}}}

{{{x^2-8x+16+49=36}}}

{{{x^2-8x+65-36=0}}}

{{{x^2-8x+29=0}}}..use quadratic formula

{{{x = (-(-8) +- sqrt( (-8)^2-4*1*29 ))/(2*1) }}}

{{{x = (8 +- sqrt(64-116 ))/2 }}}

{{{x = (8 +- sqrt(-52 ))/2 }}}

solutions: imaginary, no {{{x-intercepts}}}



{{{y-intercepts}}} occur when {{{x = 0}}}

{{{(0-4)^2+(y+7)^2=36}}}

{{{16+(y+7)^2=36}}}

{{{16+y^2+14y+49=36}}}

{{{y^2+14y+65-36=0}}}

{{{y^2+14y+29=0}}}


{{{y = (-14 +- sqrt( 14^2-4*1*29 ))/(2*1) }}}

{{{y = (-14 +- sqrt(196-116 ))/2 }}}

{{{y = (-14 +- sqrt(80 ))/2 }}}

{{{y = (-14 +- 8.94)/2 }}}

solutions:

{{{y = (-14 + 8.94)/2 }}}

{{{y = -5.06/2 }}}

{{{y = -2.53 }}}

and

{{{y = (-14-8.94)/2 }}}

{{{y = -22.94/2 }}}

{{{y = -11.47}}}





{{{drawing( 600, 600, -15, 15, -15, 15,
  grid( 1 ),
  circle( 4, -7, 0.1 ),green(circle(4,-7,6))
   ))}}}