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

Question

The co-ordinates of a focus of the hyperbola 9x2 - 16y2 + 18 x + 32y - 151 = 0 are (A) (-1, 1), (4, 1) (B)  (6, 1), (-6, 1) (C) (4, 1), (6, 1)  (D)  (- 6, 1), (4, 1)

Tardigrade Admin · Accepted Answer

Given Hyperbola 9(x2 + 2x + 1) - 16(y2 - 2y+ 1) = 151 + 9 - 16 ⇒((x+1)2/16)- ((y-1)2/9) =1 foci (4, 1), (-6, 1)

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

$(- 1, 1), (4, 1)$

$(6, 1), (- 6, 1)$

$(4, 1), (6, 1)$

$(- 6, 1), (4, 1)$

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

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

(−1,1),(4,1)

(6,1),(−6,1)

(4,1),(6,1)

(−6,1),(4,1)