SOLUTION: An ellipse with center (4, 2) and focus (7, 2) is tangent to the y-axis. Find the length of the minor axis.

Question 1065504: An ellipse with center (4, 2) and focus (7, 2) is tangent to the y-axis. Find the length of the minor axis.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The major axis,
containing center (4,2) and focus (7,2),
is part of line .
The focal distance is the distance between center and focus,
.
There is another focus on the major axis,
with .
The ellipse looks like this:
It is tangent to the y-axis
at vertex (0,2) ,
because an ellipse with a horizontal major axis
can only be tangent to a vertical line at a vertex.
So,the semi-major axis length is
the distance from that vertex to the center,
.
Ŵe know that the length of the semi-minor axis, ,
is related to and by
.
So,

.
So, the length of the minor axis is
.
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