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

Question

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

Answer 1

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 (x₁, y₁) and the line is expressed as ax + by + c = 0

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