Find The Equation Of The Parabola Whose Focus Is (1, 1) And The Directrix Is x + Y + 1 = 0.

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Question

Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.

easy

Solution

Correct option is

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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