JEE Mains · Maths · STD 11 - 9. straight line
The vertices of a triangle are \(\mathrm{A}(-1,3), \mathrm{B}(-2,2)\) and \(\mathrm{C}(3,-1)\). \(A\) new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :
- A \(x-y-(2+\sqrt{2})=0\)
- B \(-\mathrm{x}+\mathrm{y}-(2-\sqrt{2})=0\)
- C \(x+y-(2-\sqrt{2})=0\)
- D \(x+y+(2-\sqrt{2})=0\)
Answer & Solution
Correct Answer
(C) \(x+y-(2-\sqrt{2})=0\)
Step-by-step Solution
Detailed explanation
equation of \(\mathrm{AC} \rightarrow \mathrm{x}+\mathrm{y}=2\) equation of line parallel to \(\mathrm{AC} \mathrm{x}+\mathrm{y}=\mathrm{d}\) \( \left|\frac{\mathrm{d}-2}{\sqrt{2}}\right|=1 \) \( \mathrm{~d}=2-\sqrt{2}\) \(\mathrm{eq}^{\mathrm{n}}\) of new required line…
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
- Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) is reciprocal to that of the hyperbola \(2 x^2-2 y^2=1\). If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is \(................\).JEE Mains 2023 Hard
- The value of \(12 \int \limits_0^3\left|x^2-3 x+2\right| d x\) is \(.............\)JEE Mains 2023 Medium
- Let the point \(P(\alpha, \beta)\) be at a unit distance from each of the two lines \(L_{1}: 3 x-4 y+12=0\), and \(L _{2}: 8 x+6 y+11=0\). If \(P\) lies below \(L _{1}\) and above \(L_{2}\), then \(100(\alpha+\beta)\) is equal toJEE Mains 2022 Hard
- The square of the distance of the point \((-2, -8, 6)\) from the line \(\dfrac{x-1}{1} = \dfrac{y-1}{2} = \dfrac{z}{-1}\) along the line \(\dfrac{x+5}{1} = \dfrac{y+5}{-1} = \dfrac{z}{2}\) is equal to:JEE Mains 2026 Hard
- Let \(z\) be a complex number such that the real part of \(\frac{z-2 i}{z+2 i}\) is zero. Then, the maximum value of \(|\mathrm{z}-(6+8 \mathrm{i})|\) is equal to :JEE Mains 2024 Hard
- The sum of first four terms of a geometric progression \((G.P.)\) is \(\frac{65}{12}\) and the sum of their respective reciprocals is \(\frac{65}{18} .\) If the product of first three terms of the \(G.P.\) is \(1,\) and the third term is \(\alpha\), then \(2 \alpha\) is ....... .JEE Mains 2021 Hard
More PYQs from JEE Mains
- A variable \(X\) takes values \(0, 0, 2, 6, 12, 20, \ldots, n(n-1)\) with frequencies \({}^nC_0, {}^nC_1, {}^nC_2, {}^nC_3, {}^nC_4, {}^nC_5, \ldots, {}^nC_n\), respectively. If the mean of this data is \(60\), then its median is :JEE Mains 2026 Hard
- If the vertices of a hyperbola be at \((-2, 0)\) and \((2, 0)\) and one of its foci be at \((-3, 0)\), then which one of the following points does not lie on this hyperbola?JEE Mains 2019 Hard
- A scientific committee is to be formed from \(6\) Indians and \(8\) foreigners, which includes at least \(2\) Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed, isJEE Mains 2021 Medium
- If the sum of the first \(20\) terms of the series \(\log _{\left(7^{\frac{1}{2}}\right)} x+\log _{\left(7^{\frac{1}{3}}\right)} x+\log _{\left(7^{\frac{1}{4}}\right)} x+\ldots\) is \(460,\) then \(x\) is equal toJEE Mains 2020 Hard
- Let \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) be a function of \(\mathrm{x}\) satisfying \(y \sqrt{1-x^{2}}=k-x \sqrt{1-y^{2}}\) where \(k\) is a constant and \(y\left(\frac{1}{2}\right)=-\frac{1}{4} .\) Then \(\frac{d y}{d x}\) at \(x=\frac{1}{2},\) is equal to:JEE Mains 2020 Hard
- Let \(f: R -\{3\} \rightarrow R -\{1\}\) be defined by \(f(x)=\frac{x-2}{x-3} .\) Let \(g: R \rightarrow R\) be given as \(g ( x )=2 x -3\). Then, the sum of all the values of \(x\) for which \(f^{-1}( x )+ g ^{-1}( x )=\frac{13}{2}\) is equal to ...... .JEE Mains 2021 Hard