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

The straight line perpendicular from the focus to the directrix is called the axis of the conic section.

Given, focus of the parabola = (3, 3)

Equation of directrix of the parabola is 3x – 4y = 2    ...(1)

Slope of directrix of the parabola =  

Let the slope of the axis be m.

Since, axis is perpendicular to the directrix of the parabola.

Equation of the axis of the parabola is

∴ 3y – 9 = – 4x + 12

⇒ 4x + 3y = 21    ...(2)

Solving (1) and (2), we get

When , we get

Thus, the coordinate of intersection of the axis and the directrix of the parabola is .

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