JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Equation of two diameters of a circle are \(2 x-3 y=5\) and \(3 x-4 y=7\). The line joining the points \(\left(-\frac{22}{7},-4\right)\) and \(\left(-\frac{1}{7}, 3\right)\) intersects the circle at only one point \(P(\alpha, \beta)\). Then \(17 \beta-\alpha\) is equal to
- A \(2\)
- B \(4\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Centre of circle is \((1, -1)\) Equation of \(A B\) is \(7 x-3 y+10=0 \ldots\) \(....(i)\) Equation of \(\mathrm{CP}\) is \(3 x+7 y+4=0 \ldots\)\(......(ii)\) Solving \((i)\) and \((ii)\) \(\alpha=\frac{-41}{29}, \beta=\frac{1}{29} \quad \therefore 17 \beta-\alpha=2\)
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 \(\mathrm{A}=\{1,2,3, \ldots, 10\}\) and R be a relation on A such that \(\mathrm{R}=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}=2 \mathrm{~b}+1\}\). Let \(\left(\mathrm{a}_1, \mathrm{a}_2\right)\), \(\left(a_2, a_3\right),\left(a_3, a_4\right), \ldots .,\left(a_k, a_{k+1}\right)\) be a sequence of \(k\) elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :JEE Mains 2025 Medium
- If \(\alpha\) is the positive root of the equation, \(p(x)=x^{2}-x-2=0,\) then \(\lim \limits_{x \rightarrow \alpha^{+}} \frac{\sqrt{1-\cos (p(x))}}{x+\alpha-4}\) 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
- If \(\mathrm{U}_{\mathrm{n}}=\left(1+\frac{1}{\mathrm{n}^{2}}\right)\left(1+\frac{2^{2}}{\mathrm{n}^{2}}\right)^{2} \ldots\left(1+\frac{\mathrm{n}^{2}}{\mathrm{n}^{2}}\right)^{\mathrm{n}}\), then \(\lim _{n \rightarrow \infty}\left(U_{n}\right)^{\frac{-4}{n^{2}}}\) is equal to :JEE Mains 2021 Hard
- If \((2,3,9),(5,2,1),(1, \lambda, 8)\) and \((\lambda, 2,3)\) are coplanar, then the product of all possible values of \(\lambda\) is.JEE Mains 2022 Hard
- Let \(A =\{1,2,3, \ldots, 10\}\) and \(f: A \rightarrow A\) be defined as \(f( k )=\left\{\begin{array}{cl} k +1 & \text { if } k \text { is odd } \\ k & \text { if } k \text { is even }\end{array}\right.\) Then the number of possible functions \(g : A \rightarrow A\) such that \(gof=f\) is ...... .JEE Mains 2021 Medium
More PYQs from JEE Mains
- The number of words (with or without meaning) that can be formed from all the letters of the word \("LETTER"\) in which vowels never come together isJEE Mains 2020 Medium
- Let the observations \(\mathrm{x}_{\mathrm{i}}(1 \leq \mathrm{i} \leq 10)\) satisfy the equations, \(\sum\limits_{i=1}^{10}\left(x_{i}-5\right)=10\) and \(\sum\limits_{i=1}^{10}\left(x_{i}-5\right)^{2}=40\) If \(\mu\) and \(\lambda\) are the mean and the variance of the observations, \(\mathrm{x}_{1}-3, \mathrm{x}_{2}-3, \ldots ., \mathrm{x}_{10}-3,\) then the ordered pair \((\mu, \lambda)\) is equal to :JEE Mains 2020 Hard
- Let \(\alpha \beta \neq 0\) and \(A=\left[\begin{array}{ccc}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]\). If \(B=\left[\begin{array}{ccc}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha \\ -2 \alpha & 5 & -2 \beta\end{array}\right]\) is the matrix of cofactors of the elements of \(A\), then \(\operatorname{det}(A B)\) is equal to.JEE Mains 2024 Hard
- Let \(p\) and \(q\) be two positive numbers such that \(p + q =2\) and \(p ^{4}+ q ^{4}=272 .\) Then \(p\) and \(q\) are roots of the equationJEE Mains 2021 Hard
- A possible value of \(\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)\) is :JEE Mains 2021 Medium
- A set \(S\) contains \(7\) elements. A non-empty subset \(A\) of \(S\) and an element \(x\) of \(S\) are chosen at random. Then the probability that \(x \in A\) isJEE Mains 2014 Hard