If (-3, 0) is the vertex and y-axis is the directrix of a parabola, then its focus is at the point

Question

If (-3, 0) is the vertex and y-axis is the directrix of a parabola, then its focus is at the point (A) (0, -6) (B) (-6, 0) (C) (6, 0) (D) (0, 0)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/0bdccc1848db00c88f6aeb93339f147a-.png" /> Let the coordinates of focus is (h, 0). ⇒ ((h+0/2), (0+0/2))=(-3,0) ⇒ ((h/2), 0)=(-3,0) ⇒ (h/2)=-3 ⇒ h=-6 Hence, focus is (-6,0).

Q. If (-3, 0) is the vertex and y-axis is the directrix of a parabola, then its focus is at the point

(0, -6)

(-6, 0)

(6, 0)

(0, 0)

(3, 0)

Let the coordinates of focus is $(h, 0)$ .
$\Rightarrow (\frac{h + 0}{2}, \frac{0 + 0}{2}) = (- 3, 0) \Rightarrow (\frac{h}{2}, 0) = (- 3, 0)$
$\Rightarrow \frac{h}{2} = - 3 \Rightarrow h = - 6$
Hence, focus is $(- 6, 0)$ .