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Dec 4, 2018
 #1
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Dec 4, 2018
 #1
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You'll have to work through much of the algebra here yourself.

 

you have two ellipses of the same size, one centered at (k,0), the other at (0,0)

 

Looking at the geometry it must be that B is the leftmost x intercept of (xk)29+y2=1and D is the rightmost x intercept of x29+y2=1

 

B=(k3,0)D=(3,0)

 

The x coordinates of the intersections are given by(xk)2=x22kx+k2=0x=k2y=±1k236

 

the quadrilateral formed by joining these points is a rhombus, so we solve for kthat makes the corner angle 90 degreesAD=AD=(k2,1k236)(3,0)=(k23,1k236)CD=CD=(k2,1k236)(3,0)=(k23,1k236)the angle between AD and CD being 90 degreesADCD=0

 

ADCD=5k2183k+8=0

k=245 or the size zero square when k=6

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Dec 4, 2018
 #3
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Dec 4, 2018

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