MHT CET · Maths · Pair of Lines
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
- A 1 and 2
- B 0 and 2
- C 0 and -2
- D -1 and 2
Answer & Solution
Correct Answer
(B) 0 and 2
Step-by-step Solution
Detailed explanation
\(
\begin{aligned}
& \mathrm{kx}^2+\mathrm{xy}-\mathrm{y}^2=0 \\
& \therefore \mathrm{k}+\left(\frac{\mathrm{x}}{\mathrm{y}}\right)-\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^2=0
\end{aligned}
\)
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
\(
\therefore \mathrm{k}+1-1=0 \text { or } \mathrm{k}-1-1=0 \Rightarrow \mathrm{k}=0,2
\)
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