Question 678465

{{{(x-4)^2+(y-5)^2=8}}}...........1

{{{(x+1)^2+(y+2)^2=34}}}..........2
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{{{x^2-8x+16+y^2-10y+25=8}}}...........1

{{{x^2+y^2-8x-10y+41=8}}}

{{{x^2+y^2-8x-10y=-33}}}..............1a



{{{(x^2+2x+1)+(y^2+4y+4)=34}}}..........2

{{{x^2+y^2+2x+4y+5=34}}}

{{{x^2+y^2+2x+4y=29}}}............2a

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take 1a and 2a and subtract

{{{x^2+y^2-8x-10y=-33}}}..............1a


{{{x^2+y^2+2x+4y=29}}}............2a
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{{{x^2-x^2+y^2-y^2-8x-2x-10y-4y=-33-29}}}


{{{-10x-14y=-62}}}......both sides multiply by {{{-1}}}


{{{10x+14y=62}}}........solve for {{{x}}}


{{{10x=-14y+62}}}


{{{x=-14y/10+62/10}}}


{{{x=-1.4y+6.2}}}.......plug in 1a


{{{(-1.4y+6.2)^2+y^2-8(-1.4y+6.2)-10y=-33}}}.......1a..solve for {{{y}}}


{{{1.96y^2-17.36y+38.44+y^2+11.2y-49.6-10y=-33}}}


{{{2.96y^2-16.16y-11.16=-33}}}


{{{2.96y^2-16.16y+21.84=0}}}....use quadratic formula


{{{y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{y = (-(-16.16) +- sqrt((-16.16)^2-4*(2.96)*(21.84) ))/(2*2.96) }}}


{{{y = (16.16 +- sqrt(261.1456-258.586 ))/5.92 }}}


{{{y = (16.16 +- sqrt(2.5596 ))/5.92 }}}


{{{y = (16.16 +- 1.59987)/5.92 }}}


solutions:


{{{y = (16.16 + 1.59987)/5.92 }}}


{{{y =17.75987/5.92 }}}


{{{highlight(y =2.99998) }}}


and


{{{y = (16.16 - 1.59987)/5.92 }}}


{{{y =14.56013/5.92 }}}


{{{highlight(y =2.45948) }}}


now find {{{x}}}


{{{x=-1.4y+6.2}}}......plug in {{{y =2.99998 }}}


{{{x=-1.4*2.99998+6.2}}}


{{{highlight(x=2.000028)}}}


and


{{{x=-1.4y+6.2}}}......plug in {{{y =2.45948 }}}


{{{x=-1.4*2.45948+6.2}}}


{{{highlight(x=2.756728)}}}