Find an equation of the parabola described.
-Focus at (0, 21); directrix the line y = -21
A) $x ^ { 2 } = 84 y$
B) $y ^ { 2 } = 84 x$
C) $y ^ { 2 } = 21 x$
D) $x ^ { 2 } = - 84 y$

Question

Find an equation of the parabola described.
-Focus at (0, 21); directrix the line y = -21 
A) $x ^ { 2 } = 84 y$
B) $y ^ { 2 } = 84 x$
C) $y ^ { 2 } = 21 x$
D) $x ^ { 2 } = - 84 y$

Quizplus · Accepted Answer

The focus of the parabola is at (0, 21) and the directrix is y = -21, which means the parabola opens upwards. The distance from the focus to the directrix is 42 (21 - (-21)), so the focal length (p) is 42. The standard form of a parabola opening upwards is $x^2 = 4py$. Substituting p = 42 gives $x^2 = 4*42y = 168y$. However, there seems to be a mistake in my calculation as none of the options match exactly. Correcting this, since the parabola opens upwards and the focus-directrix distance is 42, the correct formula should be $x^2 = 4py$, but with p = 21 (half the distance), leading to $x^2 = 84y$, which matches option A.

Find an Equation of the Parabola Described x2=84yx ^ { 2 } = 84 yx2=84y

Find an Equation of the Parabola Described $x ^ { 2 } = 84 y$