Q84 / 150 · MHT CET 2021 (23 Sep Shift 1) · Mathematics
If one of the lines given by $k x^2+x y-y^2=0$ bisect the angle between the co-ordinate axes, then the values of $\mathrm{k}$ are
- A1 and 2
- Correct answerB0 and 2
- C0 and -2
- D-1 and 2
Solution
$$
\begin{aligned}
& \mathrm{kx}^2+\mathrm{xy}-\mathrm{y}^2=0 \\
& \therefore \mathrm{k}+\left(\frac{\mathrm{x}}{\mathrm{y}}\right)-\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^2=0
\end{aligned}
$$
Slope of line is \pm 1
$$
\therefore \mathrm{k}+1-1=0 \text { or } \mathrm{k}-1-1=0 \Rightarrow \mathrm{k}=0,2
$$
Hence, the correct answer is option: 'B'.