JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The set of values of \(k\) for which the circle \(C : 4 x^{2}+4 y^{2}-12 x+8 y+k=0\) lies inside the fourth quadrant and the point \(\left(1,-\frac{1}{3}\right)\) lies on or inside the circle \(C\) is
- A An empty set
- B \(\left(6, \frac{95}{9}\right]\)
- C \(\left[\frac{80}{9}, 10\right)\)
- D \(\left(9, \frac{92}{9}\right]\)
Answer & Solution
Correct Answer
(D) \(\left(9, \frac{92}{9}\right]\)
Step-by-step Solution
Detailed explanation
\(C : 4 x ^{2}+4 y ^{2}-12 x +8 y + k =0\) \(\Rightarrow x ^{2}+ y ^{2}-3 x +2 y +\left(\frac{ k }{4}\right)=0\) Centre \(\left(\frac{3}{2},-1\right) ; r=\sqrt{\frac{13- k }{2}} \Rightarrow k\leq13\ldots(1)\) \((i)\) Point \(\left(1, \frac{-1}{3}\right)\) lies on or inside…
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 distance of the point having position vector \( - \,\hat i\, + \,2\hat j\, + 6\hat k\) from the straight line passing through the point \((2, 3, -4)\) and parallel to the vector \(6\,\hat i\, + 3\hat j\, - 4\hat k\) isJEE Mains 2019 Easy
- The domain of the function \(f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}}\) is (where \([x]\) denotes the greatest integer less than or equal to \(x\) )JEE Mains 2023 Hard
- Let the latus ractum of the parabola \(y ^{2}=4 x\) be the common chord to the circles \(C _{1}\) and \(C _{2}\) each of them having radius \(2 \sqrt{5}\). Then, the distance between the centres of the circles \(C _{1}\) and \(C _{2}\) isJEE Mains 2020 Medium
- If the sum of the first \(n\) terms of the series \(\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ......\) is \(435\sqrt 3 \) , then \(n\) equalsJEE Mains 2017 Hard
- The locus of the mid-point of the line segment joining the focus of the parabola \(y^{2}=4 a x\) to a moving point of the parabola, is another parabola whose directrix isJEE Mains 2021 Hard
- The constant term in the expansion of \(\left(2 x+\frac{1}{x^7}+3 x^2\right)^5 \text { is }........\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- \(60\) words can be made using all the letters of the word \(BHBJO,\) with or without meaning. If these words are written as in a dictionary, then the \(50^{\text {th }}\) word is :JEE Mains 2024 Medium
- If the system of equations:
\(x+y+z=5\)
\(x+2y+3z=9\)
\(x+3y+\lambda z=\mu\)
has infinitely many solutions, then the value of \(\lambda+\mu\) is:JEE Mains 2026 Medium - Let \(x=2\) be a local minima of the function \(f(x)=2 x^4-18 x^2+8 x+12, x \in(-4,4)\). If \(M\) is local maximum value of the function \(f\) in \((-4,4)\), then \(M =\)JEE Mains 2023 Hard
- Let the mean and the variance of \(20\) observations \(x_{1}, x_{2}, \ldots x_{20}\) be \(15\) and \(9 ,\) respectively. For \(\alpha \in R\), if the mean of \(\left( x _{1}+\alpha\right)^{2},\left( x _{2}+\alpha\right)^{2}, \ldots,\left( x _{20}+\alpha\right)^{2}\) is \(178 ,\) then the square of the maximum value of \(\alpha\) is equal to \(...........\)JEE Mains 2022 Hard
- Let \(P \left( x _0, y _0\right)\) be the point on the hyperbola \(3 x ^2-4 y ^2\) \(=36\), which is nearest to the line \(3 x+2 y=1\). Then \(\sqrt{2}\left( y _0- x _0\right)\) is equal to :JEE Mains 2023 Hard
- If the tangent to the curve, \(y =f( x )= x \log _{ e } x\) \((x>0)\) at a point \((c, f(c))\) is parallel to the line segement joining the points \((1,0)\) and \(( e , e ),\) then \(c\) is equal toJEE Mains 2020 Medium