JEE Advance - Mathematics (2006 - No. 22)
The axis of a parabola is along the line $$y = x$$ and the distances of its vertex and focus from origin are $$\sqrt 2 $$ and $$2\sqrt 2 $$ respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is
$${\left( {x + y} \right)^2} = \left( {x - y - 2} \right)$$
$${\left( {x - y} \right)^2} = \left( {x + y - 2} \right)$$
$${\left( {x - y} \right)^2} = 4\left( {x + y - 2} \right)$$
$${\left( {x - y} \right)^2} = 8\left( {x + y - 2} \right)$$