Question

The axis of parabola is along the line y=x and the distance of its vertex and focus from origin are `sqrt2` and 2`sqrt2` respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is :

Answer 1

Correct Answer - A
Since, distance of vertex from origin is `sqrt(2)` and focus is `2 sqrt(2)`
`:. ` V (1,1) and f (2,2) (i.e. lying on y = x)
where, length of latusretum
`= 4a = 4 sqrt(2)`
`:.` By definition of parabola

`PM^(2) = (4a) PN)`
Where, PN is length of perpendicular upon
`x + y - 2 = 0`, i.e., tangent at vertex
`implies ((x - y)^(2))/(2) = 4 sqrt(2) ((x + y - 2)/(sqrt(2)))`
`implies (x - y)^(2) = 8 (x + y - 2)`