parabolas

Quote:

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:
$(y-y_V)^2=2\cdot p \cdot (x-x_V)$ where p is the distance between the focus and the directrix. So plug in the values you know and you'll get:

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

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