TS EAMCET · Maths · Straight Lines
If a line \(L\) passes through the point of intersection of the lines \(2 x+3 y+1=0\) and \(x+y-3=0\) and the angle made by the line \(L\) with \(X\)-axis measured in positive direction from the positive \(X\)-axis is \(\tan ^{-1} \frac{2}{3}\), then the sum of the intercepts made by this line on the axes is
- A \(\frac{-1}{41}\)
- B \(\frac{205}{6}\)
- C \(\frac{5}{41}\)
- D \(\frac{41}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{41}{6}\)
Step-by-step Solution
Detailed explanation
Let equation of required line is \(\frac{x}{a}+\frac{y}{b}=1\) ...(i) Since, Eq. (i) passes through \((10,-7)\) which is point of intersection of given lines. So, \(\frac{10}{a}-\frac{7}{b}=1\) Also given, slope…
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 ( is a real number) represents a hyperbola, then the set of all values of isTS EAMCET 2022 Easy
- Let \(\mathrm{A}=(1,2), \mathrm{B}=(2,1), \mathrm{C}=(-1,-1)\) be three points. If \(\mathrm{P}\) is a point such that the area of the quadrilateral \(\mathrm{PABC}\) is twice the area of the triangle \(\mathrm{PAB}\), then the equation of the locus of \(\mathrm{P}\) isTS EAMCET 2023 Medium
- For any integer \(n \geq 1, \sum_{K=1}^n K(K+2)=\)TS EAMCET 2017 Easy
- In a \(\triangle A B C,(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}\) is equal toTS EAMCET 2004 Medium
- If \(C_1\) and \(C_2\) are the centres of similitude with respect to the circles \(x^2+y^2+6 x+8 y+24=0\) and \(x^2+y^2-6 x-8 y\) \(+9=0\) then \(C_1 C_2=\)TS EAMCET 2022 Medium
- If the latus rectum of a hyperbola subtends an angle of \(120^{\circ}\) at its centre, then its eccentricity isTS EAMCET 2022 Easy
More PYQs from TS EAMCET
- Observe the following statements
Statement - I: Hybridisation is not same in both \(\mathrm{SF}_6\) and \(\mathrm{BrF}_5\).
Statement - II: \(\mathrm{BrF}_5\) is Square pyramidal while \(\mathrm{SF}_6\) is octahedral in shape
The correct answer isTS EAMCET 2025 Medium - A point that lies on the common tangent to the circles and among the following options isTS EAMCET 2021 Medium
- If \(y=y(x)\) is the solution of the differential equation \(\left(\frac{2+\sin x}{y+1}\right) \frac{d y}{d x}+\cos x=0 \quad\) with \(y(0)=1\), then \(y\left(\frac{\pi}{2}\right)\) is equal toTS EAMCET 2011 Medium
- TS EAMCET 2019 Medium
- If the function \(f(x)=x^3+a x^2+b x+40\) satisfies the conditions of Rolle's theorem on the interval \([-5,4]\) and \(-5,4\) are two roots of the equation \(f(x)=0\), then one of the values of c as stated in that theorem isTS EAMCET 2024 Medium
- If \(\omega\) is a complex cube root of unity, then \(225+\left(3 \omega+8 \omega^2\right)^2+\left(3 \omega^2+8 \omega\right)^2\) is equal to:TS EAMCET 2003 Hard