Find the equation of the set of all points whose distances from `(0,4)a r e2/3` of their distances from the line `y=9.`

Explanation

To find the equation of the set of all points whose distances from the point (0, 4) are \( \frac{2}{3} \) of their distances from the line \( y = 9 \), we can follow these steps:

### Step 1: Define the Point
Let the point be \( (x, y) \).

### Step 2: Calculate the Distance from the Point (0, 4)
The distance from the point \( (x, y) \) to the point \( (0, 4) \) is given by the distance formula:
\[
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