JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
For the two circles \(x^2 + y^2 = 16\) and \(x^2 + y^2 -2y = 0,\) there is/are
- A one pair of common tangents
- B two pair of common tangents
- C three pair of common tangents
- D no common tangent
Answer & Solution
Correct Answer
(D) no common tangent
Step-by-step Solution
Detailed explanation
Let, \({x^2} + {y^2} = 16\) or\({x^2} + {y^2} = {4^2}\) radius of circle \({r_1} = 4\,\) center \({C_1}\left( {0,0} \right)\) we have \({x^2} + {y^2} - 2y = 0\) or \({x^2} + {\left( {y - 1} \right)^2} = {1^2}\) Rsdius \(1\), center \({C_2}\left( {0,1} \right)\)…
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
- If the two roots of the equation \(\left( {a - 1} \right)\left( {{x^4} + {x^2} + 1} \right) + \left( {a + 1} \right){\left( {{x^2} + x + 1} \right)^2} = 0\) are real and distinct, then the set of all values of \('a'\) isJEE Mains 2015 Hard
- If a circle \(C\) passing through the point \((4, 0)\) touches the circle \(x^2 + y^2 + 4x -6y = 12\) externally at the point \((1, -1)\), then the radius of \(C\) isJEE Mains 2019 Hard
- Let \(f\) : \(A \to B\) be a function defined as \(f(x)\, = \frac{{x - 1}}{{x - 2}}\) , where \(A\, = R - \{2\}\) and \(B\, = R - \{1\}\) . Then \(f\) isJEE Mains 2018 Hard
- If the equation of the normal to the curve \(y=\frac{x-a}{(x+b)(x-2)}\) at the point \((1,-3)\) is \(x-4 y=13\), then the value of \(a+b\) is equal to \(.......\).JEE Mains 2023 Hard
- Let a curve \(y=f(x), x \in(0, \infty)\) pass through the points \(P\left(1, \frac{3}{2}\right)\) and \(Q\left(a, \frac{1}{2}\right)\). If the tangent at any point \(R(b, f(b))\) to the given curve cuts the \(y\)-axis at the point \(S(0, c)\) such that \(b c=3\), then \((P Q)^2\) is equal to \(.........\).JEE Mains 2023 Hard
- Let \([\mathrm{t}]\) denote the greatest integer \(\leq \mathrm{t}\). Then the value of \(8 \cdot \int \limits_{-\frac{1}{2}}^{1}([2 x]+|x|) \,d x\) is .... .JEE Mains 2021 Hard
More PYQs from JEE Mains
- The area (in sq. units) of the region bounded by the curve \(x^2 = 4y\) and the straight line \(x = 4y - 2\) isJEE Mains 2019 Hard
- The number of real roots of the equation, \(\mathrm{e}^{4 \mathrm{x}}+\mathrm{e}^{3 \mathrm{x}}-4 \mathrm{e}^{2 \mathrm{x}}+\mathrm{e}^{\mathrm{x}}+1=0\) isJEE Mains 2020 Hard
- Let \(\mathrm{C}\) be the set of all complex numbers. Let \(\mathrm{S}_{1} =\left\{\mathrm{z} \in \mathrm{C}|| \mathrm{z}-3-\left.2 \mathrm{i}\right|^{2}=8\right\}\) \(\mathrm{S}_{2} =\{\mathrm{z} \in \mathrm{C} \mid \operatorname{Re}(\mathrm{z}) \geq 5\} \text { and }\) \(\mathrm{S}_{3} =\{\mathrm{z} \in \mathrm{C} \| \mathrm{z}-\bar{z} \mid \geq 8\}\) Then the number of elements in \(\mathrm{S}_{1} \cap \mathrm{S}_{2} \cap \mathrm{S}_{3}\) is equal to:JEE Mains 2021 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\left(x^2+1\right) y^{\prime}-2 x y=\left(x^4+2 x^2+1\right) \cos x\), \(y(0)=1\). Then \(\int_{-3}^3 y(x) d x\) is :JEE Mains 2025 Medium
- Let \((\lambda, 2,1)\) be a point on the plane which passes through the ponit \((4,-2,2) .\) If the plane is perpendicular to the line joining the points \((-2,-21,29)\) and \((-1,-16,23),\) then \(\left(\frac{\lambda}{11}\right)^{2}-\frac{4 \lambda}{11}-4\) is equal toJEE Mains 2021 Hard
- The term independent of \(x\) in the expansion of \(\left[\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right]^{10}, x \neq 1,\) is equal to ....... .JEE Mains 2021 Hard