axis of a parabola is y=x and vertex and focus are at distance 2^(1/2) and 2*2^(1/2) respectivaly from the origin. then equation pf parabola

A)(x-y)^2=8*(x+y-2)

B) (x+y)^2=2*(x+y-2)

c) (x-y)^2=4*(x+y-2)

D) (x+y)^2=2*(x-y+2)

distance of vertex from focus & directrix is same  ...if parabola is considered in +xy plane then

vertex is at 2^1/2 away from origin ....

(x2,y2) are coordinates of vertex then

y₂-y_{1/sin@ =} x2-x1_/cos@ = d             ................1

d = 2^1/2 , (x1,y1) = (0,0)  & cos@ = 1/2^1/2  (coz slope is 1) so

y2 = 1 , x2 = 1

vertex = (1,1)

now focus by same formula 1 will be

focus = (2,2)

directrix will be perpendicular line to axis of parabola passing through origin

y = -x will be directrix

distance of focus from directrix = distance of any point on parabola to focus

(y+x)/root2 = [ (x-2)²+(y-2)² ]^1/2

y² + x² + 2xy = 2 [ x² + y² - 4x - 4y + 8 ]

x²+y² -2xy =  (8x+8y-16)

(x-y)² = 8(x+y-2)

this is the required eq ... option A) is correct

approve if u like my ans