A concave mirror forms an image I corresponding to a point object O . The equation of the circle intercepted by the xy plane on the mirror is

Explanation

From mirror equation `(1)/(v) + (1)/(u) = (1)/(f) = (1)/(-(x_(1)-25)) + (1)/(-(x_(2) + 50)) = (1)/(f)` and
from m = `-(v)/(u) = -(1)/(4) , (x_(1)-25)/(x_(1)+50) = (1)/(4) implies 4x_(1) - 100 = x_(1) + 50 implies 3x_(1) = 150 implies x_(1) = 50"unit"`

`(1)/(f) = (-1)/(50-25) + (-1)/(50 + 50) = -((1)/(25) + (1)/(100)) implies f=-20"unit" implies R = -40"unit"`
Centre of circle will be at `(10,0)`
Equation of required circle `(x-10)^(2) + (y-0)^(2) = (40)^(2) implies x^(2) + y^(2) -20x - 1500 = 0`