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in Algebraic Expressions by (25 points)

ax+by=c

x2+y2=1

Prove that bx-ay=  +- Root Over(a2 + b2 + c2)

by (13.0k points)
–1
It should be a^2 + b^2 - c^2

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1 Answer

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by (13.0k points)

Given that

ax + by = c ... (1)

x2 + y2 = 1 ... (2)

Squaring (1) on both sides, we get

⇒ a2x2 + b2y2 + 2axby = c2

⇒ a2(1 - y2) + b2(1 - x2) + 2axby = c2  (∵ x2 + y2 = 1) 

⇒ a2 - a2y2 + b2 - b2x2 + 2axby = c2

⇒ a2 + b2 - c2 = a2y2 + b2x2 - 2axby

⇒  a2 + b2 - c2 = (bx - ay)2 

∴ bx - ay = \( { \pm \sqrt{a^2 + b^2 - c^2} }\)

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