Parabola

Direction: Consider the following for the next two (02) items.

The two ends of the latus rectum of a parabola are (−2, 4) and (−2, −4).

What is the maximum number of parabolas that can be drawn through these two points as end points of latus rectum?

Consider the following statements in respect of the equation x² + 3y = 0:

 I. The equation represents equation to parab- ola that opens upwards.

 II. The axis of the parabola is x = 0.

III. The equation of the latus rectum is 4y - 3 = 0.

 How many of the statements given above are correct?

A tangent to the parabola y² = 4x is inclined at an angle of 45° with the positive direction of x-axis. What is point of contact of the tangent and the parabola?

What is the area of the parabola bounded by the latus rectum?