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 .