The equation to the pair of lines through the origin and forming an equilateral triangle with the line 4x - 3y + 1 = 0 is
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is it correct if wrong sorry
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4x - 3y + 1 = 0
We know that the standard equation ax + by + c = 0
For pair of lines
(ax+by) ^2 -3(bx -ay) ^2 = 0
Here
a=4
b=3
c=1
On substituting
(4x+3y) ^2 -3(3x -4y) ^2 = 0
16x^2 + 9y^2 + 24xy -3(9x^2 +16y^2 -24xy) = 0
16x^2 + 9y^2 + 24xy -27x^2 -48y^2 +72xy = 0
-11x^2 -39 y^2 -96 xy =0
On taking - as common
11x^2 + 39 y^2 +96 xy =0
Is the equation to the pair of lines through the origin and forming an equilateral triangle with the line 4x - 3y + 1 = 0
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