The equations of the transverse and conjugate axes of the hyperbola 16 x2-y2+64 x+4 y+44=0, are respectively

Question

The equations of the transverse and conjugate axes of the hyperbola 16 x2-y2+64 x+4 y+44=0, are respectively (A) x=2, y+2=0 (B) x=2, y=2 (C) y=2, x+2=0 (D) None of these

Tardigrade Admin · Accepted Answer

The given equation can be written as (4 x+8)2-(y-2)2=-44+64-4 arrow (16(x+2)2/16)-((y-2)2/16)=1 Transverse and conjugate axes are y=2, x=-2 arrow x+2=0

Q. The equations of the transverse and conjugate axes of the hyperbola $16 x^{2} - y^{2} + 64 x + 4 y + 44 = 0$ , are respectively

$x = 2, y + 2 = 0$

$x = 2, y = 2$

$y = 2, x + 2 = 0$

None of these

The given equation can be written as
$(4 x + 8)^{2} - (y - 2)^{2} = - 44 + 64 - 4$
$\to \frac{16 ( x + 2 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{16} = 1$
Transverse and conjugate axes are $y = 2, x = - 2$
$\to x + 2 = 0$

Q. The equations of the transverse and conjugate axes of the hyperbola 16x2−y2+64x+4y+44=0, are respectively

x=2,y+2=0

x=2,y=2

y=2,x+2=0