AP EAMCET · Maths · Straight Lines
A line \(L_1\) passing through the point of intersection of the lines \(x-2 y+3=0\) and \(2 x-y=0\) is parallel to the Line \(L_2\). If \(L_2\) passes through origin and also through the point of intersection of the lines \(3 x-y+2=0\) and \(x-3 y-2=0\), then the distance between the lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\) is
- A \(\frac{1}{\sqrt{2}}\)
- B \(\sqrt{2}\)
- C \(\sqrt{5}\)
- D \(\frac{1}{\sqrt{5}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
Intersection of \(3x-y+2=0\) and \(x-3y-2=0\): \((x,y)=(-1,-1)\) Equation of \(L_2\) (through \((0,0)\) and \((-1,-1)\)): \(y=x \implies x-y=0\) Slope of \(L_2\) is \(m_2=1\) Intersection of \(x-2y+3=0\) and \(2x-y=0\): \((x,y)=(1,2)\) Equation of \(L_1\) (through \((1,2)\)…
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 number of odd positive divisors of 67500 isAP EAMCET 2023 Easy
- If \(x>0, y>0, z>0, x y+y z+z x < 1\) and if \(\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi\), then \(x+y+z\) equals toAP EAMCET 2014 Medium
- \(\sin ^4 \frac{\pi}{8}+\cos ^4 \frac{\pi}{8}+\sin ^4 \frac{3 \pi}{8}+\cos ^4 \frac{3 \pi}{8}+\sin ^4 \frac{5 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\sin ^4 \frac{7 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=\)AP EAMCET 2017 Medium
- There are 4 hotels in a town. If 3 men check into the hotels in a day then the probability that each checks into a different hotel isAP EAMCET 2022 Easy
- If the circle \(\mathrm{S}=0\) cuts the circles \(x^2+y^2-2 x+6 y=0\). \(x^2+y^2-4 x-2 y+6=0\) and \(x^2+y^2-12 x+2 y+3=0\) orthogonally, then equation of the tangent at \((0,3)\) on \(S=\) 0 isAP EAMCET 2024 Hard
- The equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve \(x^2+x y+y^2+x+3 y+1=0\) and the line \(x+y+2=0\) isAP EAMCET 2019 Hard
More PYQs from AP EAMCET
- If \(0 < p < q\), then \(\lim _{n \rightarrow \infty}\left(q^n+p^n\right)^{1 / n}\) is equal to :AP EAMCET 2006 Medium
- Statement (A) For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero.
Statement (B) The volume contraction of a metal cube of bulk modulus \(140 \mathrm{GPa} .10 \mathrm{~cm}\) on a edge, when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\) is \(-0.05 \mathrm{~m}^3\).
Statement (C) A spiral spring is stretched by a weight attached to it. The strain is tensile.AP EAMCET 2022 Medium - In an AC circuit \(V\) and \(I\) are given below, then find the power dissipated in the circuit
\(V=50 \sin (50 t) v I=50 \sin \left(50 t+\frac{\pi}{3}\right) \mathrm{mA}\)AP EAMCET 2015 Easy - The decreasing order of priority for the following functional groups in the IUPAC Nomenclature is
\(-\mathrm{SO}_3 \mathrm{H},-\mathrm{CN},-\mathrm{COOH},-\mathrm{OH}, \mathrm{CHO}\)AP EAMCET 2023 Medium - If thenAP EAMCET 2021 Easy
- The de Broglie wavelength associated with an electron accelerated through a potential difference of \(\frac{200}{3} \mathrm{~V}\) is nearlyAP EAMCET 2025 Medium