Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.
x2 – 2xy + y2 – 6x – 6y + 3 = 0
Let P(x, y) be any point on the parabola.
Then the distance of (x, y) from the focus (1, 1).
= distance of P(x, y) from the directrix (x + y + 1 = 0)
Squaring (1), we get
or 2[x2 + 1 – 2x + y2 + 1 – 2y] = x2 + y2 + 2xy + 2y + 2x + 1
or x2 – 2xy + y2 – 6x – 6y + 3 = 0
This is the required equation of the parabola.
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