Parabola Questions

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?

Direction: Consider the following for the next two items
that follow:
The area bounded by the parabola y²= kx and
the line x = k, where k > 0, is 4/3 square units.

 What is the value of k?

Consider the points P(4k, 4k) and Q(4k, –4k) lying on the parabola y² = 4kx. If the vertex is A, then what is Angle PAQ equal to?

In the parabola y2 = 8x, the focal distance of a point P lying on it is 8 units. Which of the following statements is/are correct?

 1. The coordinates of P can be (6 , 4√3 )  .

 2. The perpendicular distance of P from the directrix of parabola is 8 units.

 Select the correct answer using the code given below:

What is the equation of directrix of parabola

y² = 4bx,

where b < 0 and b² + b − 2 = 0 ?

For the next two (02) items:

A parabola passes through (1, 2) and satisfies the differential equation

dy/dx = 2y/x, x > 0, y > 0.

What is the length of latus rectum of the parabola ?