Question 1190958

 
given:


Vertices ({{{-1}}},{{{3}}})  and ({{{5}}},{{{3}}})  =>  ->shows common {{{y}}} coordinate {{{3}}}. So {{{x}}} axis is major axis and {{{y}}} axis is minor axis, therefore {{{a}}} greater than {{{b}}}

{{{2a}}}  is the distance between vertices =>{{{2a=6}}}->{{{a=3}}}
and centre is half way between vertices: Center at ({{{2}}},{{{3}}}) ->{{{h=2}}} and {{{k=3}}}

length of minor axis  {{{4}}},  -> {{{2b=4}}} ->{{{b=2}}}

Standard equation for this ellipse is

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

your equation is:

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

{{{(x-2) ^2/9 + (y-3) ^2 /4= 1}}}


{{{ drawing(600, 600, -10, 10, -10, 10,
circle(-1,3,.12), locate(-1,3,V(-1,3)),
circle(5,3,.12), locate(5,3,V(5,3)),
circle(2,3,.12), locate(2,3,C(2,3)),
graph(600, 600, -10, 10, -10, 10, (1/3)(9 - 2sqrt(-x^2 + 4x+5)),(1/3)(2sqrt(-x^2 + 4x+5)+9))) }}}