# Parabola and Foci Problems

• Feb 20th 2011, 02:52 PM
Alyssa21
Parabola and Foci Problems
Hi, I need some help on these 2 problems:

1. What is the focus of the parabola with the equation (x-1)^2+32=8y
A. (1,4)
B. (1,2)
C. (-1,6)
D. (1,6)

2.Find the foci of an ellipse with the equation 7(x-2)^2+3(y-2)^2=21
A. (-4, -2) and (0,-2)
B. (-2,-4) and (-2,0)
C. (4,2) and (0,2)
D. (2,4) and (2,0)

Thanks =)
• Feb 20th 2011, 09:56 PM
earboth
Quote:

Originally Posted by Alyssa21
Hi, I need some help on these 2 problems:

1. What is the focus of the parabola with the equation (x-1)^2+32=8y
A. (1,4)
B. (1,2)
C. (-1,6)
D. (1,6)

2.Find the foci of an ellipse with the equation 7(x-2)^2+3(y-2)^2=21
A. (-4, -2) and (0,-2)
B. (-2,-4) and (-2,0)
C. (4,2) and (0,2)
D. (2,4) and (2,0)

Thanks =)

To #1:
The general equation of a parabola opening up is:

$(x-h)^2=4p(y-k)$

The vertex of this parabola has the coordinates V(h, k) and the focus has the coordinates F(h, k+p)

To #2:

The general equation of an ellipse is:

$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$

The center of the ellipse has the coordinates C(h, k). The focal length e is measured on the main axis (the longest of the two axes) so that the focii have the coordinates (in your case!): $F_1(h, k-e), F_2(h, k+e)$
e is calculated in your case by $e^2 + a^2 = b^2$