Question

What is the focus of the parabola 4x2 = 2y ?
1. (1/8, 0)
2. (0, 1/2)
3. (0, 1/4)
4. None of these.
5. (0, 2)

Answer 1

Correct Answer - Option 4 : None of these.

Concept:

Parabola: The locus of a point which moves such that its distance from a fixed point is equal to its distance from a fixed straight line. (Eccentricity = e = 1)

Equation	x2 = 4ay;
Vertex	(0, 0)
Focus	(0, a)
Equation of the directrix	y = -a
Equation of the axis	x = 0
Length of Latus rectum	4a
Focal distance	y + a

 

Calculation:

The given equation of the parabola 4x2 = 2y can be written as x2 = \(\frac 24\)y.

x2 = \(4 \times \frac 1 8 \times \rm y\)

Comparing this with the standard form of the equation x2 = 4ay, we get a = 1/8.

Focus of the parabola is at (0, a) = (0, 1/8).