Question 815010
Find the foci for the following hyperbola
25x^2-9y^2+100x-54y+10=0
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25x^2-9y^2+100x-54y+10=0
25x^2+100x-9y^2-54y=-10
complete the square:
25(x^2+4x+4)-9(y^2+6y+9)=-10+100-81
25(x+2)^2-9(y+3)^2=9
{{{(x+2)^2/(9/25)-(y+3)^2=1}}}
This is a hyperbola with horizontal transverse axis.
Its standard form of equation: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
For given hyperbola"
center:(-2,-3)
a^2=9/25
b^2=1
c^2=a^2+b^2=(9/25)+1=34/25
c=√34/5≈1.17
foci=(-2±c,-3)=(-2±1.17,-3)=(-3.17,-3) and (-.83,-3)