Q45 of 63 Page 202

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The equation of the parabola having focus at (–1, –2) and the directrix x – 2y + 3 = 0 is ____________ .

S = Focus = (-1, -2) & Directrix is x – 2y + 3 = 0


Let a point on the parabola be P (x,y).


So, length of perpendicular on the directrix = Distance from point (x,y) to the Focus


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


Using Distance Formula,






Squaring both the sides,




x2 + 4y2 + 9 - 4xy - 12y + 6x = 5x2 + 10x + 25 + 5y2 + 20y


4x2 + 4x + 4xy + y2 + 32y + 16 = 0
Hence the equation of parabola is 4x2 + 4x+4xy+ y2+32y+16=0


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