Let x₀ y₀ be any point on the parabola.
We will find the distance between (x₀ y₀) and the focus and then find the distance between (x₀ y₀) and the directrix,. Finally we will equate the two equations and solve for x₀ y₀
Using the distance formula
![|d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/6y55gyuxr0zmmcm1w6cs5srcfzsrudsayf.png)
The distance between (Tx₀ y) and (9,0) is
![\sqrt[]{(x_0-9)^2+(y_0-0)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/1vvvjz0oosx69zj7f6b3hhy0aab9mvcapc.png)
The distance between (x₀ y₀) and the directories x=-9 is
|tx + 9|
Next, is to equate the two expressions
t
![\sqrt[]{(x_0-9)^2+y^2_0}](https://img.qammunity.org/2023/formulas/mathematics/college/vkdr6vc8bit10mq2m3p3jxn0tt50bwk5x8.png)
the