JEE Mains · Maths · STD 11 - 9. straight line
Let a triangle be bounded by the lines \(L _{1}: 2 x +5 y =10\); \(L _{2}:-4 x +3 y =12\) and the line \(L _{3}\), which passes through the point \(P (2,3)\), intersect \(L _{2}\) at \(A\) and \(L _{1}\) at \(B\). If the point \(P\) divides the line-segment \(A B\), internally in the ratio \(1: 3\), then the area of the triangle is equal to
- A \(\frac{110}{13}\)
- B \(\frac{132}{13}\)
- C \(\frac{142}{13}\)
- D \(\frac{151}{13}\)
Answer & Solution
Correct Answer
(B) \(\frac{132}{13}\)
Step-by-step Solution
Detailed explanation
Points \(A\) lies on \(L _{2}\) \(A \left(\alpha, 4+\frac{4}{3} \alpha\right)\) Points \(B\) lies on \(L _{1}\) \(B \left(\beta, 2-\frac{2}{5} \beta\right)\) Points \(P\) divides \(AB\) internally in the ratio \(1: 3\)…
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 function \(f : N \to N\) defined by \(f\left( x \right) = x - 5\left[ {\frac{x}{5}} \right]\) , where \(N\) is set of natural numbers and \([x]\) denotes the greatest integer less than or equal to \(x\), isJEE Mains 2017 Hard
- Let the image of parabola \( x^{2}=4y \) in the line \( x-y=1 \) be \( (y+\alpha)^{2}=b(x-c), \) \( a, b, c \in \mathbb{N} \). Then \( a+b+c \) is equal toJEE Mains 2026 Hard
- The area of the region : \(R =\left\{( x , y ): 5 x ^{2} \leq y \leq 2 x ^{2}+9\right\}\) is ........ \(square\, units\)JEE Mains 2021 Hard
- In an examination, there are \(5\) multiple choice questions with \(3\) choices, out of which exactly one is correct There are \(3\) marks for each correct answer, \(-2\) marks for each wrong answer and \(0\) mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets \(5\) marks is. . . . . ... . .JEE Mains 2022 Hard
- The number of seven digit integers with sum of the digits equal to \(10\) and formed by using the digits \(1,2\) and \(3\) only isJEE Mains 2021 Medium
- If \(m\) arithmetic means \(( A . Ms )\) and three geometric means \((G.Ms)\) are inserted between \(3\) and \(243\) such that \(4^{\text {th }}\) \(A.M.\) is equal to \(2^{\text {nd }}\) \(G.M.\), then \(m\) is equal toJEE Mains 2020 Hard
More PYQs from JEE Mains
- Let \( y^{2}=12x \) be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that \( \angle OPA=90^{\circ} \). Then the locus of the centroid of such triangles OPA is :JEE Mains 2026 Easy
- The number of arrangements of the letter of the word "\(INDEPENDENCE\)" in which all the vowels always occur together isJEE Mains 2023 Medium
- Let slope of the tangent line to a curve at any point \(P ( x , y )\) be given by \(\frac{ xy ^{2}+ y }{ x } .\) If the curve intersects the line \(x+2 y=4\) at \(x=-2,\) then the value of \(y ,\) for which the point \((3, y )\) lies on the curve, is ..... .JEE Mains 2021 Hard
- Let \(\mathrm{X}=\{\mathrm{n} \in \mathrm{N}: 1 \leq \mathrm{n} \leq 50\} .\) If \(A=\{n \in X: n \text { is a multiple of } 2\}\) and \(\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n} \text { is a multiple of } 7\},\) then the number of elements in the smallest subset of \(X\) containing both \(\mathrm{A}\) and \(\mathrm{B}\) isJEE Mains 2020 Medium
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right)\) \(x > 0, y(1)=3\). Then \(\frac{y^2(x)}{9}\) is equal to :JEE Mains 2023 Hard
- Let \(\alpha, \beta\) be the roots of the equation \(x^2-a x-b=0\) with \(\operatorname{Im}(\alpha) \lt \operatorname{Im}(\beta)\). Let \(P_n=\alpha^n-\beta^n\). If \(\mathrm{P}_3=-5 \sqrt{7} i, \mathrm{P}_4=-3 \sqrt{7} i, \mathrm{P}_5=11 \sqrt{7} i\) and \(\mathrm{P}_6=45 \sqrt{7} i\), then \(\left|\alpha^4+\beta^4\right|\) is equal to __________.JEE Mains 2025 Medium