A parabola has the origin as its focus and the line x=2 as the directrix. Then the vertex of the parabola is at

Question

A parabola has the origin as its focus and the line x=2 as the directrix. Then the vertex of the parabola is at (A) (0,2) (B) (1,0) (C) (0,1) (D) (2,0)

Tardigrade Admin · Accepted Answer

Vertex of a parabola is the mid-point of focus and the point <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6eae16a199233f9dd507e7a306e727c3-.png" /> where directrix meets the axis of the parabola. Here focus is O(0,0) and directxix meets the axis at B(2,0) ∴ Vertex of the parabola is (1,0)

Q. A parabola has the origin as its focus and the line $x = 2$ as the directrix. Then the vertex of the parabola is at

(0,2)

(1,0)

(0,1)

(2,0)

Vertex of a parabola is the mid-point of focus and the point

where directrix meets the axis of the parabola.
Here focus is $O (0, 0)$ and directxix meets the axis at $B (2, 0)$
$∴$ Vertex of the parabola is $(1, 0)$

Q. A parabola has the origin as its focus and the line x=2 as the directrix. Then the vertex of the parabola is at