MHT CET · Maths · Straight Lines
From the following options, the nearest line to the origin is ....
- A \(3 x-4 y+4=0\)
- B \(2 x-3 y=5\)
- C \(4 x-3 y+12=0\)
- D \(5 x-2 y=3\)
Answer & Solution
Correct Answer
(D) \(5 x-2 y=3\)
Step-by-step Solution
Detailed explanation
For line \(3x-4y+4=0\): \(d = \frac{|4|}{\sqrt{3^2 + (-4)^2}} = \frac{4}{\sqrt{25}} = \frac{4}{5} = 0.8\) For line \(2x-3y=5 \implies 2x-3y-5=0\): \(d = \frac{|-5|}{\sqrt{2^2 + (-3)^2}} = \frac{5}{\sqrt{13}} \approx 1.386\)
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 angle between the vectors \(\bar{a}=2 \lambda^2 \hat{i}+4 \lambda \hat{j}+\hat{k}\) and \(\overline{\mathrm{b}}=7 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}\) is obtuse, then \(\lambda \in\)MHT CET 2021 Easy
- If \(y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leq x < \frac{\pi}{2}\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{6}\) isMHT CET 2021 Medium
- Find \(\frac{d y}{d x}\), if \(x=2 \cos \theta-\cos 2 \theta\) and
\(y=2 \sin \theta-\sin 2 \theta .\)MHT CET 2009 Easy - Angle of intersection of the curve \(r=\sin \theta+\cos \theta\) and \(r=2 \sin \theta\) is equal toMHT CET 2008 Easy
- If \(x^{\frac{2}{5}}+\mathrm{y}^{\frac{2}{5}}=a^{\frac{2}{5}}\) then \(\frac{\mathrm{dy}}{\mathrm{d} x}=\)MHT CET 2025 Easy
- The population \(\mathrm{P}(\mathrm{t})\) of a certain mouse species at time \(\mathrm{t}\) satisfies the differential equation \(\frac{d P(t)}{d t}=0 \cdot 5 P(t)-450 \cdot\) If \(\mathrm{P}(0)=850\), then the time at which the population becomes zero isMHT CET 2020 Medium
More PYQs from MHT CET
- Identify 'B' in the following reaction \(\mathrm{C}_{2} \mathrm{H}_{6} \underset{\mathrm{AlBr}_{3}}{\stackrel{\mathrm{Br}_{2}}{\longrightarrow}} \mathrm{A} \quad \frac{\mathrm{CH}_{3} \mathrm{COOAg}}{\Delta} \longrightarrow \mathrm{B}\)MHT CET 2020 Hard
- Which among the following salt solution in water shows \(\mathrm{pH}\) less than 7 ?MHT CET 2021 Easy
- Silver crystallises in fcc structure, if edge length of unit cell is \(316.5 \mathrm{pm}\). What is the radius of silver atom?MHT CET 2020 Easy
- \(\sin ^{-1}\left(\frac{1}{2}\right)+\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)+\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)=\)MHT CET 2020 Easy
- The equation of the pair of tangents at \((0,1)\) to the circle \(x^{2}+y^{2}-2 x-6 y+6=0\) isMHT CET 2012 Easy
- Let \(a, b \in R\). If the mirror image of the point \(\mathrm{p}(\mathrm{a}, 6,9)\) w.r.t. line \(\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}\) is \((20, b,-a-9)\), then \(|a+b|\) is equal toMHT CET 2024 Easy