The equation of the bisectors of the angle be | vedclass

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Question

(A) The given equation is $4x^2 - 16xy - 7y^2 = 0$. Comparing this with $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = -16$ (so $h = -8$),and $b = -7$.

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$8x^2 + 11xy - 8y^2 = 0$

Vedclass · Answer

(A) The given equation is $4x^2 - 16xy - 7y^2 = 0$. Comparing this with $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = -16$ (so $h = -8$),and $b = -7$. The equation of the bisectors of the angle between the lines is given by $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$. Substituting the values,we get $\frac{x^2 - y^2}{4 - (-7)} = \frac{xy}{-8}$. This simplifies to $\frac{x^2 - y^2}{11} = \frac{xy}{-8}$. Cross-multiplying gives $-8(x^2 - y^2) = 11xy$. Rearranging the terms,we get $8x^2 + 11xy - 8y^2 = 0$.

The equation of the bisectors of the angle between the lines represented by the equation $4x^2 - 16xy - 7y^2 = 0$ is

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