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  4. The co-ordinates of a focus of the hyperbola 9x2 - 16y2 + 18 x + 32y - 151 = 0 are

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Q. The co-ordinates of a focus of the hyperbola $9x^2 - 16y^2 + 18 x + 32y - 151 = 0 $ are

Conic Sections

Solution:

Given Hyperbola
$9(x^2 + 2x + 1) - 16(y^2 - 2y+ 1) $
$= 151 + 9 - 16$
$\Rightarrow\frac{\left(x+1\right)^{2}}{16}- \frac{\left(y-1\right)^{2}}{9} =1$
foci $(4, 1), (-6, 1)$