Question

In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the

parabola, the equation of the directrix and the length of the latus rectum.
y² = 12x

Answer 1

The focus of the parabola y² = 12x is at (3, 0), the axis is the x-axis, the directrix is x = -3, and the length of the latus rectum is 12 units.

Step-by-step explanation:

To find the focus, axis of the parabola, the equation of the directrix, and the length of the latus rectum for the equation y² = 12x, we can use the general form of a parabola y² = 4ax where a is the distance from the vertex to the focus (and also the distance from the vertex to the directrix). In the given equation, 4a = 12, so a = 3. Therefore, the coordinates of the focus are (3, 0), the axis of the parabola is the x-axis, the equation of the directrix is x = -3, and the length of the latus rectum, which is equal to 4a, is 12 units.