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Question
The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is ______.
Solution
The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is x2 + 16y2 + 9 – 8xy – 24y + 6x = 0.
Explanation:
Using the definition of parabola,
We have `sqrt((x - 2)^2 + (y - 3)^2) = |(x - 4y + 3)/sqrt(17)|`
Squaring, we get 17(x2 + y2 – 4x – 6y + 13) = x2 + 16y2 + 9 – 8xy – 24y + 6x
or 16x2 + y2 + 8xy – 74x – 78y + 212 = 0
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