Find the Parabola with Vertex (2,-1) and Directrix y=-1/2 (2,-1) y=-1/2

$(2, - 1)$ $y = - \frac{1}{2}$

Step 1

Since the directrix is vertical, use the equation of a parabola that opens up or down.

${(x - h)}^{2} = 4 p (y - k)$

Step 2

Find the distance from the focus to the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is $| p |$ . Subtract the value of the directrix from the $y$ coordinate of the vertex to find $p$ .

$p = - 1 + \frac{1}{2}$

Simplify.

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$p = - 1 \cdot \frac{2}{2} + \frac{1}{2}$

Combine $- 1$ and $\frac{2}{2}$ .

$p = \frac{- 1 \cdot 2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$p = \frac{- 1 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $- 1$ by $2$ .

$p = \frac{- 2 + 1}{2}$

Add $- 2$ and $1$ .

$p = \frac{- 1}{2}$

Move the negative in front of the fraction.

$p = - \frac{1}{2}$

Step 3

Substitute in the known values for the variables into the equation ${(x - h)}^{2} = 4 p (y - k)$ .

${(x - 2)}^{2} = 4 (- \frac{1}{2}) (y + 1)$

Step 4

Simplify.

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

Step 5

Find the Parabola with Vertex (2,-1) and Directrix y=-1/2 (2,-1) y=-1/2

Related Questions

Support LCMGCF.com by disabling your adblocker.