MHT CET · Maths · Pair of Lines
If the slope of one of the lines given by \(a x^2+2 h x y+b y^2=0\) is two times the other, then
- A \(8 h=9 a b^2\)
- B \(8 h^2=9 a b^2\)
- C \(8 h^2=9 a b\)
- D \(8 h=9 a b\)
Answer & Solution
Correct Answer
(C) \(8 h^2=9 a b\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{m}_1+\mathrm{m}_2=\frac{-2 \mathrm{~h}}{\mathrm{~b}} \text { and } \mathrm{m}_1+\mathrm{m}_2=\frac{\mathrm{a}}{\mathrm{b}} \\ & \Rightarrow \mathrm{m}+2 \mathrm{~m}=\frac{-2 \mathrm{~h}}{\mathrm{~b}} \text { and } \mathrm{m} \times 2 \mathrm{~m}=\frac{\mathrm{a}}{\mathrm{b}} \\ & \Rightarrow 3 \mathrm{~m}=\frac{-2 \mathrm{~h}}{\mathrm{~b}} \text { and } 2 \mathrm{~m}^2=\frac{\mathrm{a}}{\mathrm{b}} \\ & \Rightarrow 2\left(\frac{-2 \mathrm{~h}}{3 \mathrm{~b}}\right)^2=\frac{\mathrm{a}}{\mathrm{b}} \\ & \Rightarrow 8 \mathrm{~h}^2=9 \mathrm{ab}\end{aligned}\)
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
- The equation of the plane, passing through the intersection of the planes \(x+y+z=1\) and \(2 x+3 y-z+4=0\) and parallel to \(Y\)-axis isMHT CET 2024 Medium
- If \(a^2+b^2+c^2=r^2\), then the value of \(\tan ^{-1}\left(\frac{a b}{c r}\right)+\tan ^{-1}\left(\frac{b c}{a r}\right)+\tan ^{-1}\left(\frac{c a}{b r}\right)=\)MHT CET 2025 Medium
- The equation of normal to the curve \(x^{2}+y^{2}=r^{2}\) at \(p(\theta)\) isMHT CET 2010 Easy
- The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of \(\mathrm{X}\)-axis is \(30^{\circ}\), isMHT CET 2021 Medium
- The order of the differential equation whose solution is \(\mathrm{y}=\mathrm{a} \cos \mathrm{x}+\mathrm{b} \sin \mathrm{x}+\mathrm{c} \mathrm{e}^{-\mathrm{x}}\) isMHT CET 2021 Easy
- If the angle between the lines given by \(x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0\) is \(\tan ^{-1}\left(\frac{1}{3}\right)\), then the value of \(\lambda\) isMHT CET 2023 Easy
More PYQs from MHT CET
- If two curves \(x^2-4 y^2=2\) and \(8 x^2=40-\mathrm{my}^2\) are orthogonal to each other then \(\mathrm{m}=\)MHT CET 2025 Medium
- Match the category in Column-I with their description in Column-II.
Column-I Column-II i. Extinct a. Decline in species population from 50% to 70% over last 10 years. ii. Endangered b. Species that are abundant. iii. Vulnerable c. Species of its last individual has died. iv. Least concern d. Decline in species population from 30% to 50% over last 10 years. MHT CET 2022 Hard - A pendulum performs S.H.M. with period \(\sqrt{3}\) second in a stationery lift. If lift moves up with acceleration \(\frac{\mathrm{g}}{3}\), the period of pendulum is \([\mathrm{g}=\) acceleration due to gravity \(]\)MHT CET 2020 Medium
- Assuming that the junction diode is ideal, the current in the arrangement shown in figure is
MHT CET 2019 Medium - The surface tension of a soap solution is ' \(\mathrm{T}\) '. Work done in blowing a soap bubble of diameter \(2 \mathrm{~d}\) isMHT CET 2022 Easy
- A ladder of length \(17 \mathrm{~m}\) rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of \(1 \mathrm{~m} / \mathrm{sec}\)., then when it is \(8 \mathrm{~m}\) away from the wall, its upper end is coming down at the rate ofMHT CET 2023 Hard