Find the equation of the straight line passing through the pair of points (a, b) and (a + b, a-b).
A
(2b−a)x+by+(a2−b2−2ab)=0
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B
(2a−b)x+by+(a2−b2−2ab)=0
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C
(2b−a)x+ay+(a2−b2−2ab)=0
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D
(2a−b)x+by+(a2−b2−2b)=0
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Solution
The correct option is A(2b−a)x+by+(a2−b2−2ab)=0 Points are (a, b) and (a + b, a - b) So, equation of line be, y−b=a−b−ba+b−a(x−a)⇒y−b=a−2bb(x−a),⇒b(y−b)=(a−2b)(x−a)⇒by−b2=ax−a2−2bx+2ab⇒by−b2−ax+a2+2bx−2ab=0⇒(2b−a)x+by+(a2−b2−2ab)=0