Q21 of 59 Page 178

If p is the length of perpendicular from the origin on the line and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.

Given equation is


Since, p is the length of perpendicular drawn from the origin to the given line



Squaring both the sides, we have



…(i)


Since, a2, b2 and p2 are in AP


∴ 2p2 = a2 + b2



…(ii)


Form eq. (i) and (ii), we get




⇒ (a2 + b2)(a2 + b2) = 2(a2b2)


⇒ a4 + b4 + a2b2 + a2b2 = 2a2b2


⇒ a4 + b4 = 0


Hence Proved


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