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Find the equation of the parabola whose focus is (3, – 4) and directrix x – y + 5 = 0.

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Find the equation of the parabola whose focus is (3, – 4) and directrix x – y + 5 = 0.

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

⇒ (x – 3)2 + (y + 4)2 =  (x - y +  5)2/2

⇒  x2 + y2 + 2xy – 22x + 26y + 25 = 0

⇒ (x + y)2 = 22x – 26y – 25

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