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If (4, 0) is the vertex and the y-axis is the directrix of a parabola, then where is its focus?

If (4, 0) is the vertex and the y-axis is the directrix of a parabola, then where is its focus? Correct Answer (8, 0)

Concept:

Parabola:

  • A parabola is the set of all points in a plane that is equidistant from a fixed-line and fixed point (not on the line) in the plane.
  • The fixed-line is called the directrix of the parabola and the fixed point F is called the focus.

 

Calculation:

Given vertex is (4, 0) since y-axis is the directrix of a parabola,

equation of directrix is x = 0, so axis of parabola is x – axis.

Let the focus be (a, 0)

[ alt="903" src="//storage.googleapis.com/tb-img/production/18/03/903.PNG" style="height:292px; width:392px">

Distance of the vertex of a parabola from directrix = its distance from focus.

So, OV = VF

⇒ 4 = a – 4

a = 8

⇒ Focus is (8, 0)

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