COMEDK · Maths · 11. Pair of Lines
If two pairs of lines \(x^{2}-2 m x y-y^{2}=0\) and \(x^{2}-2 n x y-y^{2}=0\) are such that one of them represents the bisector of the angles between the other, then
- A \(m n=1\)
- B \(m+n=m n\)
- C \(m n=-1\)
- D \(m-n=m n\)
Answer & Solution
Correct Answer
(C) \(m n=-1\)
Step-by-step Solution
Detailed explanation
The equation of the pair of lines is \(x^{2} - 2mxy - y^{2} = 0\). The angle bisectors of this pair are given by the formula \(\dfrac{x^{2} - y^{2}}{a - b} = \dfrac{xy}{h}\). Here \(a = 1\), \(b = -1\), and \(h = -m\). Substituting these values, we get…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(|\vec{a}|=2 \sqrt{2}\) and \(|\vec{b}|=3\) and angle between \(\vec{a}\) and \(\vec{b}\) is \(\dfrac{\pi}{4}\). If a parallelogram is constructed with adjacent sides \(\vec{p}=2 \vec{a}-3 \vec{b}\) and \(\vec{q}=\vec{a}+\vec{b}\) then the product of length of both the diagonals isCOMEDK 2025 Medium
- For any vector \(\vec{p}\), the value of \(\left[2\left\{|\vec{p} \times \hat{\imath}|^2+|\vec{p} \times \hat{\jmath}|^2+|\vec{p} \times \hat{k}|^2\right\}\right]\) isCOMEDK 2025 Medium
- Integral of \(\int \dfrac{d x}{x^{2}\left[1+x^{4}\right]^{3 / 4}}\).COMEDK 2021 Hard
- The maximum value of \(n < 101\), such that \(1+\sum_{k-1}^{n} i^{k}=0\) isCOMEDK 2018 Medium
- \(\int \dfrac{(x-1)}{(x+1)^3} e^x d x=P(x)+c\) then \(P(x)=\)COMEDK 2025 Medium
- Find the particular solution of the differential equation \(x^2 d y=\left(2 x y+y^2\right) d x\) given that \(y=1\) when \(x=1\)COMEDK 2025 Medium
More PYQs from COMEDK
- The image of the point \((2,4)\) on the line \(x+y-10=0\) isCOMEDK 2012 Easy
- The number of positive divisors of 252 isCOMEDK 2020 Easy
- If \(a, b\) and \(c \in N\), which one of the following is not true?COMEDK 2016 Medium
- Which of the following electron transitions in the H-atom will release the largest amount of energy?COMEDK 2012 Hard
- An inductor and a resistor are connected to an \(\mathrm{AC}\) supply of \(50 \mathrm{~V}\) and \(50 \mathrm{~Hz}\). If the voltage across the resistor is \(40 \mathrm{~V}\), then the voltage across the inductor will beCOMEDK 2012 Easy
- Arrange the following compounds in the increasing order of their reactivity in nucleophilic addition reactions. p-nitrobenzaldehyde (I); methylphenylketone (II); benzaldehyde (III); 4-methylbenzaldehyde (IV)COMEDK 2025 Medium