Find the focus and directrix of the
following parabola:

Focus:
Directrix:

Ask by Reid Brooks. in the United States

Jan 20,2025

Question

Find the focus and directrix of the following parabola: $$ (y-4)^{2}=16(x-6) $$ Focus: $$ (10,[?]) $$ Directrix: $$ x= $$

UpStudy AI · Accepted Answer

To find the focus and directrix of the parabola given by the equation:

$$
(y - 4)^2 = 16(x - 6)
$$

Let's compare this with the standard form of a parabola that opens horizontally:

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

**Step 1: Identify the Parameters**

From the given equation:
- $$ h = 6 $$
- $$ k = 4 $$
- $$ 4p = 16 $$ ⇒ $$ p = 4 $$

**Step 2: Determine the Focus**

For a parabola that opens to the right, the focus is located at:
$$
(h + p, k) = (6 + 4, 4) = (10, 4)
$$

**Step 3: Determine the Directrix**

The directrix is a vertical line located at:
$$
x = h - p = 6 - 4 = 2
$$

**Final Answer:**
- **Focus:** $$ (10, \,4) $$
- **Directrix:** $$ x = 2 $$
Focus: $$ (10, 4) $$ Directrix: $$ x = 2 $$

Find the focus and directrix of the
following parabola:

Focus:
Directrix: