Parabola · Mathematics · NDA

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MCQ (Single Correct Answer)

1
Consider the points P(4k, 4k) and Q(4k, -4k) lying on the parabola y2 = 4kx. If the vertex is A, then what is ∠PAQ equal to?
NDA Mathematics 1st September 2024
2

In the parabola $y^2 = 8x$, 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 $\left(6, 4\sqrt{3}\right)$.

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

Select the correct answer using the code given below:

NDA Mathematics 21 April 2024
3
What is the equation of directrix of parabola y2 = 4bx, where b < 0 and b2 + b - 2 = 0?
NDA Mathematics 3 September 2023
4
An equilateral triangle is inscribed in a parabola x2 = $\sqrt{3}$y where one vertex of the triangle is at the vertex of the parabola. If p is the length of side of the triangle and q is the length of the latus rectum, then which one of the following is correct ?
NDA Mathematics 4 September 2022
5
The area of the region bounded by the parabola y2 = 4kx, where k > 0 and its latus rectum is 24 square units. What is the value of k ?
NDA Mathematics 10 April 2022
6
What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0 ?
NDA Mathematics 10 April 2022
7
What is the maximum number of parabolas that can be drawn through these two points as end points of latus rectum?
NDA Mathematics 14 November 2021
8

Consider the following statements in respect of such parabolas:

1. One of the parabolas passes through the origin (0, 0).

2. The focus of one of the parabolas lies at (-2, 0).

Which of the above statements is/are correct?

NDA Mathematics 14 November 2021
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