# If the lines represented by the equation #x^2+y^2=c^2((bx+ay)/(ab))^2# form a right angle then prove that:#1/a^2+1/b^2+1/c^2=3/c^2#?

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#1/a^2+1/b^2+1/c^2=3/c^2#

See below.

then

grouping variables gives us

#{(a^2 b^2 - a^2 c^2 - m = 0), ( m^2- 2 a b c^2 =1), (a^2 b^2 - b^2 c^2 + m=0):}#

From the first we have

from the third we have

adding those last equations we have

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