If one of the lines ax^2 + 2hxy + by^2 = 0 bi | vedclass

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(C) The angle bisector of the positive coordinate axes (the first quadrant) is the line $y = x$.Since this line is one of the lines represented by the

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$(a+b)^2=4h^2$

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(C) The angle bisector of the positive coordinate axes (the first quadrant) is the line $y = x$.Since this line is one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$,it must satisfy the equation.Substituting $y = x$ into the equation:$ax^2 + 2h(x)(x) + b(x)^2 = 0$$ax^2 + 2hx^2 + bx^2 = 0$$(a + 2h + b)x^2 = 0$For this to hold for all $x$,we must have $a + 2h + b = 0$.Therefore,$a + b = -2h$.Squaring both sides,we get $(a + b)^2 = (-2h)^2$,which simplifies to $(a + b)^2 = 4h^2$.

If one of the lines $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the positive coordinate axes,then

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