Use Ellipse For A Circle

Geometry Level 3

2 x 2 + 6 x y + 5 y 2 = 1 \large 2x^2+6xy+5y^2=1

Find r 2 r^2 , where r r is the radius of auxilliary circle of the given ellipse.


The answer is 6.85410195.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Orrin Hobbs
May 16, 2018

I used desmos.com to plot the graph, then estimated the point which the curve ends, which was 2.2165,1.3889 . This tells you the lengths of two sides of a right angle. We can use pythagoras to work out the square of the hypotenuse of this line, which is r . 2.2165^2+1.3889^2=4.91287225+1.92904321=6.84191546

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