Question

: The focus for this parabola is (3, 0)

x^2 = 12y

A: True
B: False

: The equation of the directrix for this parabola is x = - 2

1
x = - --- y^2
8
A: True
B: False

Answer 1

Answer on Question #57313 – Math – Analytic Geometry

Question

1. The focus for this parabola is $(3, 0)$

$$x^2 = 12y$$

A: True

B: False

Solution

The standard form of the equation of a parabola with vertex at the origin and a vertical axis is

$$x^2 = 4py$$

The focus is at point $(0, p)$.

For parabola $x^2 = 12y$ the vertex is at $(0,0)$, $4p = 12$, hence $p = 3$. Then the focus is at $(0, p) = (0,3)$.

**Answer:** B: False

Question

2. The equation of the directrix for this parabola is $x = -2$

$$x = -\frac{1}{8}y^2$$

A. True

B. False

Solution

The standard form of the equation of a parabola with vertex at the origin and a horizontal axis is

$$y^2 = 4px$$

The focus is at point $(p, 0)$, the equation of directrix is $x = -p$.

If $x = -\frac{1}{8}y^2$, then $y^2 = -8x$, $4p = -8$, hence $p = -2$. For this parabola the vertex is at $(0,0)$, the focus is at $(-2,0)$, the equation of directrix is $x = 2$.

**Answer:** B: False.

www.AssignmentExpert.com