Question 1180257


The equation {{{(y-2)^2/3^2-(x-2)^2/4^2=1}}} represents a hyperbola whose 

foci are (?,?) and (?,?)

{{{(y-2)^2/3^2-(x-2)^2/4^2=1}}} =>Up-down  hyperbola, {{{h=2}}},{{{k=2}}}, {{{a=3}}}, {{{b=4}}}

foci: (?,?) 
For an up-down facing hyperbola, the foci  (focus points ) are defined as  ({{{h}}}, {{{k+c}}} ), ({{{h}}}, {{{k-c }}})

options for first set of ?'s

 ({{{h}}}, {{{k+c}}} )

we need to calculate {{{c}}}

{{{c=sqrt(a^2+b^2)}}}
{{{c=sqrt(3^2+4^2)}}}
{{{c=sqrt(9+16)}}}
{{{c=sqrt(25)}}}
{{{c=5}}}

then foci is at  ({{{2}}}, {{{2+5}}} )=> ({{{2}}}, {{{7}}} )

answer: b. ({{{2}}},{{{7}}})


options for second set of ?'s

({{{2}}}, {{{2-5}}})=>({{{2}}}, {{{-3 }}})

answer: a. ({{{2}}},{{{-3}}})