The parametric equations of the parabola y2-4 x-8 y-12=0 are

Question

The parametric equations of the parabola y2-4 x-8 y-12=0 are (A) x=7+2 t, y=-4+t2 (B) x=-7+2 t, y=4+2 t (C) x=-7+t2, y=-4+2 t (D) x=-7+t2, y=4+2 t

Tardigrade Admin · Accepted Answer

Given equation of parabola, y2-4 x-8 y-12=0 or y2-8 y+16=4 x+28 (y-4)2=4(x+7) Comparing with Y2=4 a X Y=y-4, a=1, X=x+7 parametric form of Y2=4 a X X=a t2, Y=2 a t ⇒ x+7=t2, y-4=2 t or x=-7+t2, y=4+2 t

Q. The parametric equations of the parabola $y^{2} - 4 x - 8 y - 12 = 0$ are

$x = 7 + 2 t, y = - 4 + t^{2}$

$x = - 7 + 2 t, y = 4 + 2 t$

$x = - 7 + t^{2}, y = - 4 + 2 t$

$x = - 7 + t^{2}, y = 4 + 2 t$

Q. The parametric equations of the parabola y2−4x−8y−12=0 are

x=7+2t,y=−4+t2

x=−7+2t,y=4+2t

x=−7+t2,y=−4+2t

x=−7+t2,y=4+2t

Given equation of parabola, y2−4x−8y−12=0 or y2−8y+16=4x+28 (y−4)2=4(x+7) Comparing with Y2=4aX Y=y−4,a=1,X=x+7 parametric form of Y2=4aX X=at2,Y=2at ⇒x+7=t2,y−4=2t or x=−7+t2,y=4+2t

Q. The parametric equations of the parabola $y^{2} - 4 x - 8 y - 12 = 0$ are

$x = 7 + 2 t, y = - 4 + t^{2}$

$x = - 7 + 2 t, y = 4 + 2 t$

$x = - 7 + t^{2}, y = - 4 + 2 t$

$x = - 7 + t^{2}, y = 4 + 2 t$