I need to determine the equation of an ellipse with vertices at (6,0) and (-6,0) containing the point (5,1). I know the center is (0,0), and that a=6, but I need to determine b or c.  Suggestions?

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Darren -Always keep plugging along using ALL the information provided in the problem.  Once you input all the provided information, sit back and see where you stand.For example, you know the general equation for an ellipse centered at (0,0), correct?  So, let's start with that:You know this ellipse contains a point (x,y) equal to (5,1).  You also know that a=6.Now sit back and look at the pieces you know and identify what you can solve for.  I believe we can solve for b in the general ellipse equation, right?  Take a close look ... we have x, y and a. so we can solve for b.Once you solve for b, then you can easily solve for c.  Remember the formula for the distance from the center of an ellipse to a focus is c defined as follows:I'll leave it for you to do the math.  Hope that helps