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Step-by-step explanation: According to question 4q2 = p2+ 3r2.
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We have to prove 4b^2=a^2+3r^2
We have to prove 4b^2=a^2+3r^2Let AC =q then AB=2q
Now take OE perpendicular to AC and OF perpendicular to AB.
In∆ OEA,
OA^2 = OE^2 + AE^2
r^2=b^2+ a^2/4
4r^2=4b^2+q^2
q^2=4r^2 - 4b^2 ....... eq 1
In ∆ OFA,
OA^2=OF^2+AF^2
r^2 = a^2 +q^2
q^2= r^2 -a^2. .........eq 2
Now by eq 1 and eq 2 ,we can write
r^2-a^2=4r^2 -4b^2
then,
4b^2=3r^2+a^2.
Hence proved.
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