Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3,3) and directrix is `3x-4y=2.` Find also the length of the latus rectum.

Explanation

Given: Focus `= (3, 3)`

Directrix `= 3x – 4y = 2`
Firstly let us find the slope of the directrix. The slope of the line `ax + by + c = 0` is `–a/b` So, `m_1 = -3/-4 = 3/4`.

Let us assume the slope of axis is `m_2`.

`m_1.m_2 = -1`

` 3/4 . m_2 = -1`

`m_2 = -4/3`

We know that the equation of the line passing through the point `(x_1, y_1)` and having slope m is `(y – y_1) = m(x – x_1)`

We know that the equation of the line passing through the point `(x_1, y_1)` and having slope m is `(y – y_1) = m(x – x_1)`
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