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# Using a directrix of y = -2 and a focus of (1, 6), what quadratic function is created?

**Solution:**

Given directrix of y = -2 and focus (1, 6)

From any point (x, y) on the parabola the focus and directrix are equidistant

We are using distance formula √{(x - 1)^{2 }+ (y - 6)^{2}} = |y + 2|

Applying square on both sides

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

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

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

⇒ -16y + 32 = -(x - 1)^{2}

⇒ -16y = -(x - 1)^{2} - 32

⇒ y = (x - 1)^{2} /16 + 32/16

⇒ y = (x - 1)^{2} /16 + 2

The quadratic equation created is y= (x - 1)^{2} /16 + 2.

## Using a directrix of y = -2 and a focus of (1, 6), what quadratic function is created?

**Summary:**

Using a directrix of y = -2 and a focus of (1, 6), y = (x - 1)^{2} /16 + 2 quadratic function is created.

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