TS EAMCET · Maths · Application of Derivatives
A variable straight-line \(L\) with negative slope passes through the point \((4,9)\) and cuts the positive coordinate axes in A and B. If O is the origin, then the minimum value of \(\mathrm{OA}+\mathrm{OB}\) is
- A \(25\)
- B \(12\)
- C \(13\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(25\)
Step-by-step Solution
Detailed explanation
Let the line be \(\frac{x}{a} + \frac{y}{b} = 1\). It passes through \((4,9)\): \(\frac{4}{a} + \frac{9}{b} = 1\). We want to minimize \(\mathrm{OA} + \mathrm{OB} = a+b\). \(a+b = (a+b)\left(\frac{4}{a} + \frac{9}{b}\right)\)…
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 \(\theta\) is the angle between the curves \(x y=2\) and \(x^2+4 y=0\) and \(x^2+4 y=0\), then \(\tan \theta\) is equal to :TS EAMCET 2006 Medium
- The extreme values of \(4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)\) over \(R\), areTS EAMCET 2005 Medium
- The equation of the circle which touches the circle \(x^2+y^2-6 x+6 y+17=0\) externally and having the lines \(x^2-3 x y-3 x+9 y=0\) as two normals, isTS EAMCET 2018 Medium
- A bag contains \(n\) white and \(n\) black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is 14400 , then \(n\) is equal toTS EAMCET 2011 Medium
- If \(D(2,1,0), E(2,0,0)\) and \(F(0,1,0)\) are mid-points of the sides \(B C, C A\) and \(A B\) of \(\triangle A B C\), respectively. Then, the centroid of \(\triangle A B C\) isTS EAMCET 2013 Medium
- Let \(L\) be the line parallel to the vector \(\sqrt{2} \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and passing through the point A given by \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\). If the distance between \(A\) and a point \(P\) on the line \(L\) is 18 units, then the position vector of such a point \(P\) isTS EAMCET 2019 Medium
More PYQs from TS EAMCET
- \(\mathrm{CaOCl}_2+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{Ca}\left(\mathrm{OH}_2+X\right.\) \(\begin{aligned} X+\mathrm{CH}_3 \mathrm{CHO} & \longrightarrow Y \ Y+\mathrm{Ca}(\mathrm{OH})_2 & \longrightarrow \mathrm{CHCl}_3 .\end{aligned}\) What is ' \(Y\) '?TS EAMCET 2007 Hard
- Which of the following statements is false during adsorption of gas molecule on a metal surface?TS EAMCET 2021 Easy
- If the product of the lengths of the perpendiculars drawn from the point \((-1,5)\) to the pair of lines \(2 x^2-x y+k y^2+6 x+y+4=0\) is \(\frac{65}{\sqrt{26}}\), then \(37 k^2+92 k\) is equal toTS EAMCET 2021 Easy
- A rocket lifts off from the ground and accelerates upwards at . seconds after liftoff a piece breaks off from the bottom of the rocket. After breaking off, how much time it takes approximately to reach the ground? (Take )TS EAMCET 2021 Medium
- If \(\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+\mathrm{c}\) then \(f(1)+g(1)=\)TS EAMCET 2025 Medium
- Let \([x]\) be greatest integer function. Then, \(\int_1^1[x+2[x+2[x]]] d x=\)TS EAMCET 2019 Easy