Question 1045863
{{{ 4x^2 +16y^2 =64 }}}.............(1)
{{{ 2x-y^2=-4 }}}.............(2).........both sides multiply by {{{16}}}
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{{{ 4x^2 +16y^2 =64 }}}.............(1)
{{{ 32x-16y^2= -64 }}}.............(2)
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{{{ 4x^2 +16y^2 +32x-16y^2=64 -64}}}

{{{ 4x^2 +cross(16y^2) +32x-cross(16y^2)=0}}}

{{{ 4x^2  +32x=0}}}................both sides divide by {{{4}}}

{{{ x^2  +8x=0}}}...........factor


{{{ x(x  +8)=0}}}

solutions:
{{{ x=0}}}
if {{{ x  +8=0}}}->{{{x=-8}}}

now find {{{y}}}

go to {{{ 2x-y^2=-4 }}}.............(2) substitute  {{{x}}}

if {{{ x=0}}} we have {{{ 2*0-y^2=-4 }}}-> {{{ -y^2=-4 }}-> {{{ 4=y^2 }}->{{{y=2}}} or {{{y=-2}}}

so, if {{{x=0}}} there are two intersection points : 

({{{0}}},{{{2}}}) and ({{{0}}},{{{-2}}}) 

if {{{ x=-8}}} we have {{{ 2*(-8)-y^2=-4 }}}-> {{{ -16-y^2=-4 }}}-> {{{ -16+4=y^2 }}}->{{{ -12=y^2 }}}->{{{y=sqrt(-12)}}} or {{{y=-sqrt(-12)}}} -> complex solutions 

{{{y=2i*sqrt(3)}}} or {{{y=-2i*sqrt(3)}}}



{{{drawing( 600, 600, -10, 10, -10, 10,
circle(0,2,.12),circle(0,-2,.12),
locate(0.1,2.4,p(0,2)),locate(0.1,-2.2,p(0,-2)),
 graph( 600, 600, -10, 10, -10, 10, sqrt((64-4x^2)/16), -sqrt((64-4x^2)/16),sqrt(2x+4),-sqrt(2x+4))) }}}