Equation of the directrix of the parabola whose focus is ( 0 , 0 ) and the tangent at the vertex is x - y + 1 = 0 is

Step-by-step solution

We have, x - y + 1 = 0       . . . i Focus is ( 0 , 0 ) . Perpendicular distance from ( 0 , 0 ) to ( i ) is given by d = 0 - 0 + 1 1 2 + 1 2 = 1 2 Now, equation of directrix is given by x - y + c = 0 [ ∵ directrix is parallel to tangent at vertex ] Perpendicular distance from ( 0 , 0 ) to directrix is 0 - 0 + c 1 2 + 1 2 = 2 1 2 ⇒ c 2 = 2 2 ⇒ c = 2 Hence, equation of directrix is x - y + 2 = 0 .