The area of the triangle formed by pair of lines ax+by2-3bx-ay2=0 and the line ax+by+c=0 is

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c2a2+b2

c22a2+b2

c23a2+b2

c22a2+b2

answer is C.

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Detailed Solution

The area of the equilateral triangle formed by the lines ax+by+c=0 and the pair of lines passing through the origin is c23(a2+b2)given lines ax+by+c=0 ……….(1)By splitting the combined equation ax+by2-3bx-ay2=0ax+by+3bx-ay=0a+3bx+b-3ay=0 …………..(2)ax+by-3bx-ay=0a-3bx+b+3ay=0 ………….(3)Solving (1) and (2) vertex is A=cb-3a3a2+b2,-ca+3b3a2+b2Solving (2) and (3) , vertex is 0=0,0Solving (3) and (1) Vertex is B=-cb+3a3a2+b2,ca+3b3a2+b2 Areaofthetriangle OAB=12x,y2−x2y1=c23a2+b2 squareunits

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