COMEDK · Maths · 10. Straight Lines
The lines represented by \(a x^{2}+2 h x y+b y^{2}=0\) are perpendicular to each other if
- A \(h=0\)
- B \(h^{2}=a b\)
- C \(a+b=0\)
- D \(h^{2}=a+b\)
Answer & Solution
Correct Answer
(C) \(a+b=0\)
Step-by-step Solution
Detailed explanation
We know that the angle between the two lines \(a x^{2}+2 h x y+b y^{2}=0\) is given by \(\tan \theta=\left|\frac{2 \sqrt{h^{2}-a b}}{a+b}\right|\) \(\begin{aligned} \because & \theta &=90^{\circ} \\ & \therefore & a+b &=0 \end{aligned}\)
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 the vectors \(\mathrm{a}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}} ; \mathrm{b}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}\) and \(\mathrm{c}=m \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) are coplanar, then the value of \(m\) isCOMEDK 2023 Medium
- If the position vector of a point \(A\) is \(\vec{a}+2 \vec{b}\) and \(\vec{a}\) divides \(A B\) in the ratio \(2: 3\), then the position vector of \(B\) isCOMEDK 2023 Easy
- The general solution of the differential equation \(x \dfrac{d y}{d x}=y+x \tan \left(\dfrac{y}{x}\right)\) isCOMEDK 2024 Medium
- If \(A(\operatorname{adj} A)=\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2\end{array}\right]\), then \(|\operatorname{adj} A|\) equalsCOMEDK 2021 Easy
- If \(a>b>0\), then the value of \(\tan ^{-1}\left(\frac{a}{b}\right)+\tan ^{-1}\left(\frac{a+b}{a-b}\right)\) depends onCOMEDK 2016 Easy
- The co-axial system of circles given by \(x^{2}+y^{2}+2 g x+c=0\) for \(c < 0\) representsCOMEDK 2013 Hard
More PYQs from COMEDK
- Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from bag A and put into bag B. However if tail appears then 2 balls are drawn at random from bag A and put into bag B. Now one ball is drawn at random from bag B. Given that the drawn ball from B is white, the probability that head appeared on the coin isCOMEDK 2023 Hard
- Match reactions in Column I with the corresponding products formed as given in Column II.
Column I Column II A. \(\text{C}_6\text{H}_5\text{N}_2^+\ \text{Cl}^- + \dfrac{\text{H}_2\text{O}}{warm} \rightarrow\) P. p–Bromophenol B. \(\text{C}_6\text{H}_5\text{OH} + \dfrac{\text{Br}_2\ \text{in}\ \text{CS}_2}{273K} \rightarrow\) Q. 2,4,6–Tribromophenol C. \(\text{C}_6\text{H}_5\text{OH} + \dfrac{(i)\ \text{CHCl}_3 + \text{NaOH}(aq)}{(ii)\ \text{HCl}} \rightarrow\) R. Phenol D. \(\text{C}_6\text{H}_5\text{OH} + \text{Br}_2\ (aq) \rightarrow\) S. 2–Hydroxybenzaldehyde COMEDK 2026 Medium - A biconvex lens has two different refractive indices in different regions. The upper half has a refractive index 1.7 and the lower half has a refractive index 1.5 . The radius of curvatures of the two surfaces are \(R_1=15 \mathrm{~cm}\) and \(R_2=-25 \mathrm{~cm}\). Image of a distant object will be formed at:COMEDK 2025 Medium
- Minimum mumber of nodes are present inCOMEDK 2022 Medium
- \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3}+\) Heat. What is the effect of the increase of temperature on the equilibrium of the reaction?COMEDK 2017 Easy
- A body of mass \(10 \mathrm{mg}\) is moving with a velocity of \(100 \mathrm{~ms}^{-1}\). The wavelength of de-Broglie wave associated with it would be
( \(\left.h=6.63 \times 10^{-34} \mathrm{Js}\right)\)COMEDK 2020 Medium