Question 1197335

the given data: 

foci at: ({{{-3}}}, {{{1}}}) and ({{{7}}},{{{1}}})

the center is half way between foci, so

C({{{(-3+7)/2}}},{{{(1+1)/2}}})=({{{2}}},{{{1}}})

=>{{{h=2}}} and {{{k = 1}}}

transverse axis is {{{4}}}: the transverse axis of a hyperbola is along the x-axis and its length is{{{ 2a}}}, so

{{{2a=4}}}
{{{a=2}}}

The equation of a hyperbola so far is:

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

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


The following equation take into account different properties of a hyperbola: 

{{{(h+3)^2=a^2+b^2}}}

{{{(2+3)^2=2^2+b^2}}}

{{{ 25=4+b^2}}}

{{{ 25-4=b^2}}}

{{{b^2= 21}}}


and your equation is:


{{{(x-2)^2/4-(y-1)^2/21=1}}}


{{{ drawing( 600, 600, -10, 10, -10, 10,
circle(-3,1,.12),circle(7,1,.12),
locate(-3,1,F(-3,1)),locate(7,1,F(7,1)),
graph( 600, 600, -10, 10, -10, 10,(1/2)(2-sqrt(21)*sqrt(x^2- 4x)), (1/2)(sqrt(21)*sqrt(x^2-4x)+2))) }}}