Find the equation of each of the following parabolas
Focus at (–1, –2), directrix x – 2y + 3 = 0
Focus = (–1, –2), directrix is x – 2y + 3 = 0
For any point (x,y) on parabola, the distance from focus to 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 i.e.., x - 2y + 3 = 0 & point = (x,y)
Distance between the point of intersection & centre = 
[Distance Formula]
Squaring both the sides,
x2 + 4y2 + 9 - 4xy + 6x - 12y = 5 [x2 + 2x + 1 + y2 + 4y + 4]
x2 + 4y2 + 9 - 4xy + 6x- 12y = 5x2 + 10x + 5y2 + 20y + 25
4x2 + y2 + 4xy + 4x + 32y + 16 =0
Hence the required equation is 4x2 + y2 + 4xy + 4x + 32y + 16 = 0