10. Find the co-ordinates of foci of the hyperbola
9x2-16 y2 - 108x-160 y= 220.
(UP 2006, 13)
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9x²-16y²-108x-160y=220
9x²-108x+324-(16y²+160y+400)=220+324-400
(3x-18)²-(4y+20)²=144
9(x-6)²-16(y+5)²=144
(x-6)²/16 - (y+5)²/9 = 1
It is of the form (x-h)/a² - (y-k)/b² = 1, where focii are (h+c,k) and (h-c,k)
=> Focii are (11,-5) and (1,-5)..
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