# Derive the Equation of the Parabola with a Focus at (6, 2) and a directrix of y = 1.

**Solution:**

Focus at (6, 2) and a directrix of y = 1

Consider (x, y) as the point on the parabola

Distance from focus (6, 2) is √(x - 6)^{2} + (y - 2)^{2}

Distance from directrix y = 1 is |y - 1|

Equation of the parabola will be √(x - 6)^{2} + (y - 2)^{2} = |y - 1|

By squaring on both sides,

(x - 6)^{2} + (y - 2)^{2} = (y - 1)^{2}

Expanding using the formulas

x^{2} - 12x + 36 + y^{2} - 4y + 4 = y^{2} - 2y + 1

So we get,

x^{2} - 12x - 2y + 39 = 0

Therefore, the equation of the parabola is x^{2} - 12x - 2y + 39 = 0.

## Derive the Equation of the Parabola with a Focus at (6, 2) and a directrix of y = 1.

**Summary:**

The equation of the parabola with a Focus at (6, 2) and a directrix of y = 1 is x^{2} - 12x - 2y + 39 = 0.

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