Question 1190884

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

center at ({{{3}}},{{{2}}}) ,{{{ h=3}}}, {{{k=2}}}

 vertices: ({{{h}}},{{{k-b}}}), ({{{h}}},{{{k+b}}})
 
given ({{{3}}}, {{{- 5}}}) and {{{k=2}}}=>{{{2-b=-5}}}->{{{b=7}}}

 focus is at ({{{h}}}, {{{k + c}}}) = ({{{3}}}, {{{7}}}) ->{{{k+c=7}}}
and, since {{{k=2}}}, {{{c=5}}}

find {{{a}}}

{{{a=sqrt(7^2-5^2)=sqrt(24) =2sqrt(6)}}}

equation is:

{{{(x-3)^2/24+(y-2)^2/49=1}}}



{{{drawing ( 600, 600, -15, 15, -15, 15,
circle(3, 2,.15),locate(3, 2,C(3,2)),
circle(3, 7,.15),locate(3, 7,F(3,7)),
circle(3, -5,.15),locate(3, -5,V(3,-5)),
graph( 600, 600, -15, 15, -15, 15, (1/12)(24-7sqrt(6)* sqrt(-x^2+6x+15)) ,(1/12)(7sqrt(6)* sqrt(-x^2+6x+15)+24) )) }}}