JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the tangent to the circle \(C _{1}: x^{2}+y^{2}=2\) at the point \(M (-1,1)\) intersect the circle \(C _{2}\) : \(( x -3)^{2}+(y-2)^{2}=5\), at two distinct points \(A\) and \(B\). If the tangents to \(C _{2}\) at the points \(A\) and \(B\) intersect at \(N\), then the area of the triangle \(ANB\) is equal to
- A \(\frac{1}{2}\)
- B \(\frac{2}{3}\)
- C \(\frac{1}{6}\)
- D \(\frac{5}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{6}\)
Step-by-step Solution
Detailed explanation
\(OP =\left|\frac{2-3+2}{\sqrt{2}}\right|\) \(OP =\frac{3}{\sqrt{2}}\) \(AP =\sqrt{ OA ^{2}- OP ^{2}}\) \(=\frac{1}{\sqrt{2}}\) \(\tan \theta=3\) \(\therefore \sin \theta=\frac{3}{\sqrt{10}}=\frac{ AP }{ AN }\) \(\Rightarrow AN =\frac{\sqrt{5}}{3}= BN\) Area of…
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
- The value of the definite integral \(\int_{\pi / 24}^{5 \pi / 24} \frac{d x}{1+\sqrt[3]{\tan 2 x}} \text { is }\)JEE Mains 2021 Hard
- Suppose \(f\) is a function satisfying \(f ( x + y )= f ( x )+ f ( y )\) for all \(x , y \in N\) and \(f (1)=\frac{1}{5}\). If \(\sum \limits_{n=1}^m \frac{f(n)}{n(n+1)(n+2)}=\frac{1}{12}\), then \(m\) is equal to \(...............\).JEE Mains 2023 Hard
- Let \({f_k}\,(x)\, = \frac{1}{k}({\sin ^k}\,x\, + \,{\cos ^k}\,x)\) for \(k=1,2,3,...\) Then for all \(x \in R,\) the value of \(f_4(x) - f_6 (x)\) is equal toJEE Mains 2019 Hard
- Let \(A=\{(x, y): 2 x+3 y=23, x, y \in N\}\) and \(B=\{x:(x, y) \in A\}\). Then the number of one-one functions from \(\mathrm{A}\) to \(\mathrm{B}\) is equal to ................JEE Mains 2024 Medium
- The coefficient of \(x^{-5}\) in the binomial expansion of \({\left( {\frac{{x + 1}}{{{x^{\frac{2}{3}}} - {x^{\frac{1}{3}}} + 1}} - \frac{{x - 1}}{{x - {x^{\frac{1}{2}}}}}} \right)^{10}}\) where \(x \ne 0, 1\) , isJEE Mains 2017 Hard
- Let \( X=\{x\in\mathbb{N}:1\le x\le19\} \) and for some \( a, b\in\mathbb{R}, Y=\{ax+b:x\in X\}. \) If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b isJEE Mains 2026 Medium
More PYQs from JEE Mains
- If the mean and the variance of \(6,4, a, 8, b, 12,10\), 13 are 9 and 9.25 respectively, then \(a+b+a b\) is equal to :JEE Mains 2025 Medium
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{ dy }{ dx }+\frac{1}{ x ^{2}-1} y =\left(\frac{ x -1}{ x +1}\right)^{\frac{1}{2}}\), \(x>1\) passing through the point \(\left(2, \sqrt{\frac{1}{3}}\right)\). Then \(\sqrt{7} y (8)\) is equal to.JEE Mains 2022 Hard
- If the surface area of a sphere of radius \(r\) is increasing uniformly at the rate \(8\, cm^2/s\), then the rate of change of its volume isJEE Mains 2013 Hard
- If \(a _{1}(>0), a _{2}, a _{3}, a _{4}, a _{5}\) are in a G.P., \(a _{2}+ a _{4}=2 a _{3}+1\) and \(3 a _{2}+ a _{3}=2 a _{4}\), then \(a _{2}+ a _{4}+2 a _{5}\) is equal toJEE Mains 2022 Hard
- The value of the integral \(\int \limits_{-\log _{ e } 2}^{\log _e 2} e^x\left(\log _0\left(e^x+\sqrt{1+e^{2 x}}\right)\right) d x\) is equal toJEE Mains 2023 Hard
- Let \(a\) and \(b\) be any two numbers satisfying \(\frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} = \frac{1}{4}\). Then, the foot of perpendicular from the origin on the variable line, \(\frac{x}{a} + \frac{y}{b} = 1\) , lies onJEE Mains 2014 Hard