NDA Mathematics 13 April 2025 | Parabola Question 1 | Mathematics

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

(1, 1)

$(2,2\sqrt{2})$

$(\frac{1}{2},\frac{1}{\sqrt{2}})$

(1,2)

NDA Mathematics 1st September 2024

MCQ (Single Correct Answer)

+2.5

-0.833

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?

60°

90°

120°

135°

NDA Mathematics 21 April 2024

MCQ (Single Correct Answer)

+2.5

-0.83

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:

1 only

2 only

Both 1 and 2

Neither 1 nor 2

NDA Mathematics 3 September 2023

MCQ (Single Correct Answer)

+2.5

-0.83

What is the equation of directrix of parabola y2 = 4bx, where b < 0 and b2 + b - 2 = 0?

x + 1 = 0

x - 2 = 0

x - 1 = 0

x + 2 = 0

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