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For 0 < k < 6, the graphs of (x - k)^2/4 + y^2 = 1 and (x + k)^2/4 + y^2 = 1 intersect at A and C, and have x-intercepts at B and D respectively. Compute the value of k for which ABCD is a square.

 

 Feb 27, 2021
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How have you tried to tackle this guest?

 

 

For    \(0

 

\(\frac{(x-k)^2}{4}+\frac{y^2}{1}=1\qquad and \qquad \frac{(x+k)^2}{4}+\frac{y^2}{1}=1\)

 

 

What are the centres of each of these ellipses?

What can you say about these two ellipses?  What is the same and what is different?

 

So if you draw both of them on the same graph, what line will they have to cross on?

 

What is the length of the semi-major axis for each.

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What are the properties of a square?  Which might be the most helpful?

 

Sketch what I have talked about so far.  See what you can work out for yourself.

 

I would like you to interact with me. Tell me what you have done and ask questions.

 

The next step is yours.

 

This will help though.

 Mar 1, 2021

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