The parametric equations for the conic section x2-8 x-4 y2-16 y-4=0 text are

Question

The parametric equations for the conic section x2-8 x-4 y2-16 y-4=0 text are  (A) x=-4+2 sec θ, y=2+ tan θ (B) x=4+2 tan θ, y=-2+ sec θ (C) x=-4+2 tan θ, y=2+ sec θ (D)  x=4+2 sec θ, y=-2+ tan θ

Tardigrade Admin · Accepted Answer

(x-4)2-16-4(y2+4 y)=4 (x-4)2-4[(y+2)2-4]=20 (x-4)-4(y+2)2=4 ((x-4)2/4)-((y+2)2/1)=1 text which is a hypererbola x-4=2 sec θ ⇒ x=4+2 sec θ text and y+2= tan θ ⇒ y=-2+ tan θ ⇒ (D)

Q. The parametric equations for the conic section
$x^{2} - 8 x - 4 y^{2} - 16 y - 4 = 0 are$

$x = - 4 + 2 sec θ, y = 2 + tan θ$

$x = 4 + 2 tan θ, y = - 2 + sec θ$

$x = - 4 + 2 tan θ, y = 2 + sec θ$

$x = 4 + 2 sec θ, y = - 2 + tan θ$

Q. The parametric equations for the conic section x2−8x−4y2−16y−4=0 are

x=−4+2secθ,y=2+tanθ

x=4+2tanθ,y=−2+secθ

x=−4+2tanθ,y=2+secθ

x=4+2secθ,y=−2+tanθ

(x−4)2−16−4(y2+4y)=4 (x−4)2−4[(y+2)2−4]=20 (x−4)−4(y+2)2=4 4(x−4)2​−1(y+2)2​=1 which is a hypererbola x−4=2secθ⇒x=4+2secθ and y+2=tanθ⇒y=−2+tanθ⇒(D)

Q. The parametric equations for the conic section
$x^{2} - 8 x - 4 y^{2} - 16 y - 4 = 0 are$

$x = - 4 + 2 sec θ, y = 2 + tan θ$

$x = 4 + 2 tan θ, y = - 2 + sec θ$

$x = - 4 + 2 tan θ, y = 2 + sec θ$

$x = 4 + 2 sec θ, y = - 2 + tan θ$