# Math Help - Ellipses

1. ## Ellipses

You're given that the center is at (1,2); focus at (1,4); passing through the point (2,2)

You need to find the equation for the ellipse and graph it.

My problem is that I'm not sure how to find a and b with the given information. I've already found that c = 2, since the distance from the center to the focus is c, and 4 -2 = 2.

I've also found that since the center = (h,k), h =1 and k = 2. Now I'm not sure what to do next to find a and b.

2. ## Re: Ellipses

Originally Posted by Smugleaf
You're given that the center is at (1,2); focus at (1,4); passing through the point (2,2)

You need to find the equation for the ellipse and graph it.

My problem is that I'm not sure how to find a and b with the given information. I've already found that c = 2, since the distance from the center to the focus is c, and 4 -2 = 2.

I've also found that since the center = (h,k), h =1 and k = 2. Now I'm not sure what to do next to find a and b.
The major axis of the ellipse is parallel to the y axis. The minor parallel to the x axis.
The ellipse passes through (2,2)
The center is at (1,2)

so what's the semi-minor axis b?

to find the semi-major axis use
$$c^2=a^2-b^2$$