JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Two circles with equal radii intersecting at the points \((0, 1)\) and \((0, -1).\) The tangent at the point \((0, 1)\) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is
- A \(1\)
- B \(2\)
- C \(2\sqrt 2\)
- D \(\sqrt 2\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
The two circle will be orthogonal \(OB=1\) \(\therefore \) \(OA=OB=OD=1\) \( \Rightarrow \) \(AB=2\)
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
- A circle passes through \((-2, 4)\) and touches the \(y-\) axis at \((0, 2).\) Which one of the following equations can represent a diameter of this circle ?JEE Mains 2016 Hard
- The length of the perpendicular drawn from the point \((2, 1, 4)\) to the plane containing the lines \(\vec r = \left( {\hat i + \hat j} \right) + \lambda \left( {\hat i + 2\hat j - \hat k} \right)\,\) and \(\vec r = \left( {\hat i + \hat j} \right) + \mu \left( { - \hat i + \hat j - 2\hat k} \right)\) isJEE Mains 2019 Hard
- If the curve \(y = f(x)\) passes through the point \((1, e)\) and satisfies the differential equation \(dy = y(2 + \log_e x)\,dx\), \(x > 0\), then \(f(e)\) is equal to :JEE Mains 2026 Medium
- Shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}\) and \(\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\) isJEE Mains 2023 Easy
- The remainder on dividing \(1+3+3^{2}+3^{3}+\ldots+3^{2021}\) by \(50\) isJEE Mains 2022 Hard
- Consider the lines \(L _1\) and \(L _2\) given by \(L_1: \frac{ x -1}{2}=\frac{ y -3}{1}=\frac{ z -2}{2}\) \(L _2: \frac{ x -2}{1}=\frac{ y -2}{2}=\frac{ z -3}{3}\) A line \(L _3\) having direction ratios \(1,-1,-2\), intersects \(L _1\) and \(L _2\) at the points \(P\) and \(Q\) respectively. Then the length of line segment \(PQ\) isJEE Mains 2023 Medium
More PYQs from JEE Mains
- The sum of the co-efficients of all odd degree terms in the expansion of \({\left( {x + \sqrt {{x^3} - 1} } \right)^5} + {\left( {x - \sqrt {{x^3} - 1} } \right)^5},\left( {x > 1} \right)\)JEE Mains 2018 Hard
- The function/ defined by \(f(x)\, = x^3 - 3x^2 + 5x + 7\), isJEE Mains 2017 Hard
- Let the coefficients of three consecutive terms \(T_r, T_{r+1}\) and \(T_{r+2}\) in the binomial expansion of \((a+b)^{12}\) be in a G.P. and let \(p\) be the number of all possible values of \(r\). Let \(q\) be the sum of all rational terms in the binomial expansion of \((\sqrt[4]{3}+\sqrt[3]{4})^{12}\). Then \(\mathrm{p}+\mathrm{q}\) is equal to :JEE Mains 2025 Medium
- Let \(\lambda_1, \lambda_2\) be the values of \(\lambda\) for which the points \(\left(\frac{5}{2}, 1, \lambda\right)\) and \((-2,0,1)\) are at equal distance from the plane \(2 x+3 y-6 z+7=0\). if \(\lambda_1 > \lambda_2\), then the distance of the point \(\left(\lambda_1-\lambda_2, \lambda_2, \lambda_1\right)\) from the line \(\frac{x-5}{1}=\frac{y-1}{2}=\frac{z+7}{2}\) is \(............\).JEE Mains 2023 Hard
- Two dices are rolled. If both dices have six faces numbered \(1,2,3,5,7\) and \(11,\) then the probability that the sum of the numbers on the top faces is less than or equal to \(8\) isJEE Mains 2021 Medium
- A bag contains \(6\) white and \(4\) black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:JEE Mains 2023 Medium