Find the equation of the set of all points whose distances from (0,4) are `2/3` 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 variables
Let the variable point be \( (h, k) \). The fixed point is \( (0, 4) \) and the line is given by \( y = 9 \).

### Step 2: Write the distance from the point to the fixed point
The distance \( S_p \) from the point \( (h, k) \) to the point \( (0, 4) \) is given by the formula:
\[
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