TS EAMCET · Maths · Circle
The line \(x+y+1=0\) intersects the circle \(x^2+y^2-4 x+2 y-4=0\) at the points A and B. If \(M\) \((a, b)\) is the midpoint of AB , then \(a-b=\)
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(x+y+1=0 \Rightarrow y=-x-1\) Solving for point of intersection \(\begin{aligned} & x^2+(-x-1)^2-4 x+2(-x-1)-4=0 \\ & 2 x^2-4 x-5=0 ; x_1+x_2=2 \Rightarrow \frac{x_1+x_2}{2}=a=1 \\ & a+b+1=0 \Rightarrow b=-2 \therefore a-b=3 \end{aligned}\)
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 \(A X=D\) be a system of three linear non-homogeneous equations. If \(|A|=0\) and \(\operatorname{rank}(A)=\operatorname{rank}([A D])=\alpha\), thenTS EAMCET 2019 Easy
- The mid-point of the chord of the circle \(x^2+y^2-6 x+4 y-12=0\) drawn parallel to the tangent at \((-1,1)\) and at a distance of one unit from the tangent isTS EAMCET 2020 Hard
- A particle moves along the curve \(y=x^2+2 x\). Then, the point on the curve such that \(x\) and \(y\) coordinates of the particle change with the same rate isTS EAMCET 2004 Easy
- \(\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots(2)\right]^{1 / n}=\)TS EAMCET 2024 Medium
- If all the letters of the word 'HANDLE' are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word 'HELAND' isTS EAMCET 2025 Medium
- The order and degree of the differential equation \(\frac{d^2 y}{d x^2}+y+\left(\frac{d y}{d x}-\frac{d^3 y}{d x^3}\right)^{3 / 2}=0\), are respectively.TS EAMCET 2020 Easy
More PYQs from TS EAMCET
- In Sun, the important source of energy isTS EAMCET 2007 Easy
- If thenTS EAMCET 2021 Easy
- Identity in the following reactionTS EAMCET 2021 Hard
- Four electric charges \(2 \mu \mathrm{C}, \mathrm{Q}, 4 \mu \mathrm{C}\) and \(12 \mu \mathrm{C}\) are placed on \(x\)-axis at distances \(x=0\), \(1 \mathrm{~cm}, 2 \mathrm{~cm}\) and 4 cm respectively. If the net force acting on the charge at origin is zero, then \(\mathrm{Q}=\)TS EAMCET 2025 Medium
- If \(\mathrm{A}=(1,-1,2), \mathrm{B}=(3,4,-2), \mathrm{C}=(0,3,2)\) and \(\mathrm{D}=(3,5,6)\) then the angle between the lines \(\overrightarrow{A B}\) and \(\overrightarrow{C D}\) isTS EAMCET 2023 Easy
- Find out the hybridisations of \(\mathrm{C}_1, \mathrm{C}_2\) and \(\mathrm{C}_3\) labelled carbon atoms in the given molecule
TS EAMCET 2020 Medium