JEE Mains · Maths · STD 11 - 9. straight line
The base of an equilateral triangle is along the line given by \(3x + 4y\,= 9\). If a vertex of the triangle is \((1, 2)\), then the length of a side of the triangle is
- A \(\frac{{2\sqrt 3 }}{{15}}\)
- B \(\frac{{4\sqrt 3 }}{{15}}\)
- C \(\frac{{4\sqrt 3 }}{{5}}\)
- D \(\frac{{2\sqrt 3 }}{{5}}\)
Answer & Solution
Correct Answer
(B) \(\frac{{4\sqrt 3 }}{{15}}\)
Step-by-step Solution
Detailed explanation
Shortes distance of a point \(\left( {{x_1},{y_1}} \right)\) from line \(ax + by = c\) is \(d = \frac{{a{x_1} + b{y_1} - c}}{{\sqrt {{a^2} + {b^2}} }}\) Now shortest distance of \(P(1,2)\) from \(3x+4y=9\) is…
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 \(y=y(x)\) be the solution of the differential equation \(x\sqrt{1-x^2}\,dy + \left(y\sqrt{1-x^2} - x\cos^{-1}x\right)dx = 0\), \(x \in (0, 1)\), \(\displaystyle\lim_{x\to 1^-} y(x) = 1\). Then \(y\left(\dfrac{1}{2}\right)\) equals:JEE Mains 2026 Medium
- If the mean of the frequency distribution
is \(28\) , then its variance is \(........\).Class: \(0-10\) \(10-20\) \(20-30\) \(30-40\) \(40-50\) Frequency \(2\) \(3\) \(x\) \(5\) \(4\) JEE Mains 2023 Hard - A tangent is drawn to the parabola \(y^{2}=6 x\) which is perpendicular to the line \(2 x + y =1\) Which of the following points does \(NOT\) lie on it ?JEE Mains 2021 Medium
- Let \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j} \neq 0\) for all \(i, j\) and \(A^2=I\). Let a be the sum of all diagonal elements of \(A\) and \(b =| A |\), then \(3 a ^2+4 b ^2\) is equal toJEE Mains 2023 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(x \log _e x \frac{d y}{d x}+y=x^2 \log _e x,(x > 1)\). If \(y (2)=2\), then \(y ( e )\) is equal toJEE Mains 2023 Hard
- If \(A\) and \(B\) are two events such that \(P(A \cap B)=0.1\), and \(P(A \mid B)\) and \(P(B \mid A)\) are the roots of the equation \(12 x^2-7 x+1=0\), then the value of \(\frac{\mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}})}{\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})}\) is :JEE Mains 2025 Hard
More PYQs from JEE Mains
- The number of points of discontinuity of the function \(f(\mathrm{x})=\left[\frac{\mathrm{x}^2}{2}\right]-[\sqrt{\mathrm{x}}], \mathrm{x} \in[0,4]\), where \([\cdot]\) denotes the greatest integer function is ________JEE Mains 2025 Easy
- The distance of the line \(\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}\) from the point \((1,4,0)\) along the line \(\frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}\) is :JEE Mains 2025 Hard
- Let the system of linear equations \(x+y+k z=2\) ; \(2 x+3 y-z=1\) ; \(3 x+4 y+2 z=k\) , have infinitely many solutions. Then the system \(( k +1) x +(2 k -1) y =7\) ; \((2 k +1) x +( k +5) y =10 \text { has : }\)JEE Mains 2023 Hard
- If the sum of squares of all real values of \(\alpha\), for which the lines \(2 x-y+3=0,6 x+3 y+1=0\) and \(\alpha x+2 y-2=0\) do not form a triangle is \(p\), then the greatest integer less than or equal to \(\mathrm{p}\) is \(.........\)JEE Mains 2024 Medium
- If \(X = \{ {4^n} - 3n - 1:n \in N\} \) and \(Y = \{ 9(n - 1):n \in N\} ,\) then \(X \cup Y\) = . . . . .JEE Mains 2014 Medium
- The distance of the point \((-1,2,3)\) from the plane \(\vec{r} .(\hat{i}-2 \hat{j}+3 \hat{k})=10\) parallel to the line of the shortest distance between the lines \(\overrightarrow{ r }=(\hat{ i }-\hat{ j })+\lambda(2 \hat{i}+\hat{ k })\) and \(\overrightarrow{ r }=(2 \hat{ i }-\hat{ j })+\mu(\hat{i}-\hat{j}+\hat{ k })\) is :JEE Mains 2023 Hard