Search any question & find its solution
Question:
Answered & Verified by Expert
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
Options:
Solution:
1783 Upvotes
Verified Answer
The correct answer is:
0 and 2
$$
\begin{aligned}
& \mathrm{kx}^2+\mathrm{xy}-\mathrm{y}^2=0 \\
& \therefore \mathrm{k}+\left(\frac{\mathrm{x}}{\mathrm{y}}\right)-\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^2=0
\end{aligned}
$$
Slope of line is \pm 1
$$
\therefore \mathrm{k}+1-1=0 \text { or } \mathrm{k}-1-1=0 \Rightarrow \mathrm{k}=0,2
$$
\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
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.