If the vertex of the parabola is the point (–3, 0) and the directrix is the line x + 5 = 0, then its equation is

Vertex = (-3, 0) & Directrix is x + 5 = 0 (Intersection point is (-5, 0)

As , the co-ordinates of focus is the mid – point of the co-ordinates of vertex & the point of intersection of directrix and x or y axis respectively.

Focus = (p,q)

p = -1 & q = 0

Focus is (-1, 0)

For any point on parabola, P(x,y) the distance of focus from that point is always equal to the perpendicular distance from that point to the directrix.

Perpendicular Distance (Between a point and line) = , whereas the point is and the line is expressed as ax + by + c = 0 x + 5 = 0

Using Distance Formula,

Squaring both the sides,

x² + 2x + 1 + y² = x² + 25 + 10x

y² = 8x + 24

y² = 8 (x + 3)

Hence the required equation is y² = 8 (x + 3).

OPTION (A) is the correct answer.