1. Find the equation of a parabola with vertex at (1,5) and focus (-5.5).

2. Find the equation of an ellipse with endpoints of the minor axis (10,2) and (10,8) and major axis of length 24.

2. Originally Posted by Brooke
1. Find the equation of a parabola with vertex at (1,5) and focus (-5.5).
2. Find the equation of an ellipse with endpoints of the minor axis (10,2) and (10,8) and major axis of length 24.
Hello, Brooke,

1. I assume that there is typo and you actually mean that the focus has the coordinates (-5,5).

2. The general equation of a parabola with axis parallel to the coordinate axis is:
$\displaystyle (y-y_V)^2=2\cdot p \cdot (x-x_V)$ where p is the distance between the focus and the directrix. So plug in the values you know and you'll get:

$\displaystyle (y-5)^2=2\cdot (-12) \cdot (x-1)$

3. The axises of the ellipse are parallel to the coordinate axises. The centre of the ellipse is thus M(10,5). So the endpoints of the major axis are at L(-2,5) and R(22,5)

Greetings

EB