As the axis of parabola is along the line y=x, the coordinates of focus and vertèx are (h,h) and (k,k) respectively. Distance of vertex from origin is √2. ⇒‌‌k2+k2=2⇒k=1 Distance of focus from origin =2√2. ‌‌h2+h2=8⇒h2=4⇒h=2 ‌ Vertex ‌≡(1,1)‌, focus ‌≡(2,2) ‌ Directrix passes through ‌(0,0)‌ and perpendicular ‌ ‌ to ‌y=x ∴‌ Directrix is ‌x+y=0 ∴‌ Parabola is ‌(x−2)2+(y−2)2=‌
(x+y)2
2
⇒‌‌(x−y)2+16=8(x+y) ‌ which is satisfied by ‌x=(t+1)2,y=(t−1)2