Find the equation of the parabola with vertex at (0,0) and focus at (0,2).

Question

Find the equation of the parabola with vertex at (0,0) and focus at (0,2). (A) x2 = 8y (B) x2 = 2y (C) y2 = 4x (D) y2 = 8x

Tardigrade Admin · Accepted Answer

Since the vertex is at (0, 0) and the focus is at (0, 2) which lies on y-axis, the y-axis is the axis of the parabola. Therefore, equation of the parabola is of the form x2 = 4ay, thus, we have x2 = 4(2)y, i.e., x2 = 8 y.

Q. Find the equation of the parabola with vertex at $(0, 0)$ and focus at $(0, 2)$ .

$x^{2} = 8 y$

$x^{2} = 2 y$

$y^{2} = 4 x$

$y^{2} = 8 x$

Since the vertex is at $(0, 0)$ and the focus is at $(0, 2)$ which lies on $y$ -axis, the $y$ -axis is the axis of the parabola. Therefore, equation of the parabola is of the form $x^{2} = 4 a y$ , thus, we have $x^{2} = 4 (2) y$ , i.e., $x^{2} = 8 y$ .

Q. Find the equation of the parabola with vertex at (0,0) and focus at (0,2).

x2=8y

x2=2y

y2=4x

y2=8x