The equation of the parabola with vertex at the origin and directrix y = 2 is

Question

The equation of the parabola with vertex at the origin and directrix y = 2 is (A) y2 = 8x (B) y2 = - 8x (C) y2=√8 x (D) x2 = - 8 y

Tardigrade Admin · Accepted Answer

Since directrix of parabolais y = 2 ⇒ y-2=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/85b9c6ed409656aee3c4ce13d9ed1026-.png" /> So, vertex of parabola is (0, 0) and focus S is (0, -2). So, equation of parabola will be x2 = - 4 ay ⇒ x2 = - 4 × 2 y = - 8 y.

Q. The equation of the parabola with vertex at the origin and directrix $y = 2$ is

$y^{2} = 8 x$

$y^{2} = - 8 x$

$y^{2} = 8 x$

$x^{2} = - 8 y$

Since directrix of parabolais $y = 2$
$\Rightarrow y - 2 = 0$

So, vertex of parabola is $(0, 0)$ and focus $S$ is $(0, - 2)$ . So, equation of parabola will be $x^{2} = - 4 a y$
$\Rightarrow x^{2} = - 4 \times 2 y = - 8 y$ .

Q. The equation of the parabola with vertex at the origin and directrix y=2 is

y2=8x

y2=−8x

y2=8​x

x2=−8y

Since directrix of parabolais y=2 ⇒y−2=0 So, vertex of parabola is (0,0) and focus S is (0,−2). So, equation of parabola will be x2=−4ay ⇒x2=−4×2y=−8y.

Q. The equation of the parabola with vertex at the origin and directrix $y = 2$ is

$y^{2} = 8 x$

$y^{2} = - 8 x$

$y^{2} = 8 x$

$x^{2} = - 8 y$

Since directrix of parabolais $y = 2$
$\Rightarrow y - 2 = 0$

So, vertex of parabola is $(0, 0)$ and focus $S$ is $(0, - 2)$ . So, equation of parabola will be $x^{2} = - 4 a y$
$\Rightarrow x^{2} = - 4 \times 2 y = - 8 y$ .