JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Suppose that two chords, drawn from the point \((1, 2)\) on the circle \(x^2 + y^2 + x - 3y = 0\) are bisected by the \(y\)-axis. If the other ends of these chords are \(R\) and \(S\), and the mid point of the line segment \(RS\) is \((\alpha, \beta)\), then \(6(\alpha + \beta)\) is equal to:
- A \(1\)
- B \(3\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
Let the other end of the chord be \((x_1, y_1)\). Since the chord is bisected by the \(y\)-axis, the midpoint of the chord lies on the \(y\)-axis. The midpoint of the chord joining \((1, 2)\) and \((x_1, y_1)\) is \(\left(\dfrac{x_1 + 1}{2}, \dfrac{y_1 + 2}{2}\right)\). Since it…
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
- Given an \(A.P.\) whose terms are all positive integers. The sum of its first nine terms is greater than \(200\) and less than \(220\). If the second term in it is \(12\), then its \(4^{th}\) term isJEE Mains 2014 Hard
- Let \(a_{1}, a_{2} \ldots, a_{n}\) be a given \(A.P.\) whose common difference is an integer and \(S _{ n }= a _{1}+ a _{2}+\ldots+ a _{ n }\) If \(a_{1}=1, a_{n}=300\) and \(15 \leq n \leq 50,\) then the ordered pair \(\left( S _{ n -4}, a _{ n -4}\right)\) is equal toJEE Mains 2020 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x\) such that \(\mathrm{y}(0)=\frac{5}{4}\). Then \(12\left(\mathrm{y}\left(\frac{\pi}{4}\right)-\mathrm{e}^{-2}\right)\) is equal to _______.JEE Mains 2025 Medium
- Let \(A :\{1,2,3,4,5,6,7\}\). Define \(B =\{ T \subseteq A\) : either \(1 \notin T\) or \(2 \in T \}\) and \(C = \{ T \subseteq A : T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set \(B \cup C\) is \(\dots\dots\)JEE Mains 2022 Hard
- Let \(x=x(t)\) and \(y=y(t)\) be solutions of the differential equations \(\frac{\mathrm{dx}}{\mathrm{dt}}+\mathrm{ax}=0\) and \(\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm{by}=0\) respectively, \(\mathrm{a}, \mathrm{b} \in \mathrm{R}\). Given that \(x(0)=2 ; y(0)=1\) and \(3 y(1)=2 x(1)\), the value of \(t\), for which \(x(t)=y(t)\), is :JEE Mains 2024 Hard
- If \(\overrightarrow {{{\left| c \right|}^2}} = 60\) and \(\overrightarrow c \times \left( {\hat i + 2\hat j + 5\hat k} \right) = \overrightarrow 0 \), then a value of \(\overrightarrow c .\left( { - 7\hat i + 2\hat j + 3\hat k} \right)\) isJEE Mains 2014 Hard
More PYQs from JEE Mains
- For some \(n \neq 10\), let the coefficients of the 5 th, 6 th and 7 th terms in the binomial expansion of \((1+\mathrm{x})^{\mathrm{n}+4}\) be in A.P. Then the largest coefficient in the expansion of \((1+\mathrm{x})^{\mathrm{n}+4}\) is:JEE Mains 2025 Medium
- The integral \(\int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin 2 x\right)} d x\) is equal toJEE Mains 2022 Hard
- If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral isJEE Mains 2019 Hard
- The integral \(\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}\) is equal to :JEE Mains 2024 Medium
- Let \(f(x)=\left|(x-1)\left(x^{2}-2 x-3\right)\right|+x-3, x \in R\). If \(m\) and \(M\) are respectively the number of points of local minimum and local maximum of \(f\) in the interval \((0,4)\), then \(m + M\) is equal toJEE Mains 2022 Hard
- If \(z_1, z_2, z_3 \in C\) are the vertices of an equilateral triangle, whose centroid is \(\mathrm{z}_0\), then \(\sum_{\mathrm{k}=1}^3\left(\mathrm{z}_{\mathrm{k}}-\mathrm{z}_0\right)^2\) is equal toJEE Mains 2025 Medium