Question 1191031


 

given:

center at ({{{4}}},{{{-1}}}) 
transverse axis parallel to the {{{y}}} axis, 
distance between foci {{{10}}}
 latus rectum {{{4/3}}}



{{{(x-h)^2/a^2-(y-k )^2/b^2=1}}}

given: 

Center at ({{{4}}},{{{-1}}})=>{{{h=4}}}, {{{k=-1}}}

latus rectum {{{(2b^2)/a=4/3}}}=>  {{{2b^2=4}}}->{{{b^2=2 }}}and {{{ a=3}}}

{{{c=sqrt(9+2)=sqrt(11)}}}

distance between foci {{{10}}} 

equation is:

{{{(x-4)^2/9-(y+1 )^2/2=1}}}



{{{ drawing( 600, 600, -10, 15, -10, 10,
circle(4,-1,.12),locate(4,-1,C(4,-1)),
graph( 600, 600, -10, 15, -10, 10, (1/3)(-sqrt(2) sqrt(x^2 - 8x+7) - 3),  (1/3)(sqrt(2) sqrt(x^2-8x+7)-3) )) }}}