Answer :

Given the equation of directrix is x + y = 3 and focus is (- 2, 1).



We know that the directrix and axis are perpendicular to each other. The axis also passes through the focus.


Let us find the slope of the directrix.


We know that the slope of the line ax + by + c = 0 is .



m1 = - 1.


We know that the products of the slopes of the perpendicular lines (non - vertical) is - 1. Let us assume the slope of axis be m2.


m1.m2 = - 1


- 1.m2 = - 1


m2 = 1.


We know that the equation of the line passing through the point (x1, y1) and having slope m is (y - y1) = m(x - x1)


y - 1 = 1(x - (- 2))


y - 1 = x + 2


x - y + 3 = 0


On solving the lines x - y + 3 = 0 and x + y = 3, we get the intersection point to be (0, 3).


We know that vertex is the mid - point of focus and point of intersection of axis and directrix.


Let (x1, y1) be the vertex of the parabola.




(x1, y1) = (- 1, 2)


The correct option is C

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