Question

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

• A. $8x^2+11xy-8y^2$
• B. $8x^2-11xy-8y^2$
• C. $16x^2+11xy-16y^2$
• D. $16x^2+11xy+16y^2$

Answer 1

The correct option is A

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

Explanation of correct answer :

Finding the equation of the bisectors of the angle between lines :

Given, the equation of pair of lines, $4x^2-16xy-7y^2=0$

As we know, the equation of pair of straight lines, $a{x}^2+2hxy+b{y}^2=0$

Comparing the given equation with this equation, we get,

$$\begin{gathered} a=4,b=-7 \\ 2h=-16 \\ \Rightarrow h=-8 \end{gathered}$$

We know that bisectors are $\frac{x^2-y^2}{a-b}=\frac{xy}{h}$

$$\begin{gathered} \Rightarrow \frac{x^2-y^2}{4-\left(-7\right)}=\frac{xy}{-8} \\ \Rightarrow \frac{x^2-y^2}{11}=-\frac{xy}{8} \\ \Rightarrow 8\left(x^2-y^2\right)=-11xy \\ \Rightarrow 8x^2-8y^2+11xy=0 \end{gathered}$$

Hence, the equation of bisectors of the angle between lines is $8x^2+11xy-8y^2$.

Thus, the correct answer is option(A).