TS EAMCET · Maths · Circle
If the circles \(x^2+y^2-2 x-2(3+\sqrt{7}) y+8+6 \sqrt{7}=0\) and \(x^2+y^2-8 x-6 y+k^2=0, k \in \mathbf{Z}\), have exactly two common tangents, then the number of possible values of \(k\) is
- A 8
- B 5
- C 9
- D 11
Answer & Solution
Correct Answer
(C) 9
Step-by-step Solution
Detailed explanation
The centres of the given circles are \(C_1(1,3+\sqrt{7})\) and \(C_2(4,3)\) and corresponding radii are \(r_1=\sqrt{1^2+(3+\sqrt{7})^2-(8+6 \sqrt{7})}=3\) and \(r_2=\sqrt{4^2+3^2-k^2}=\sqrt{25-k^2}\) Now, \(C_1 C_2=\sqrt{(4-1)^2+(3-3-\sqrt{7})^2}=4\) Clearly,…
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 \(\mathrm{A}=(1,2), \mathrm{B}=(2,1), \mathrm{C}=(-1,-1)\) be three points. If \(\mathrm{P}\) is a point such that the area of the quadrilateral \(\mathrm{PABC}\) is twice the area of the triangle \(\mathrm{PAB}\), then the equation of the locus of \(\mathrm{P}\) isTS EAMCET 2023 Medium
- The differential equation corresponding to the family of curves given by where and are arbitrary constants isTS EAMCET 2022 Easy
- \(e^{\int_0^{\pi / 2} \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x}=\)TS EAMCET 2018 Easy
- \(\operatorname{sech}^{-1}\left(\frac{3}{5}\right)-\tanh ^{-1}\left(\frac{3}{5}\right)=\)TS EAMCET 2024 Hard
- \(\int_0^{\frac{\pi}{2}} \sqrt{\tan x} d x=\)TS EAMCET 2025 Medium
- \(\int\left(\frac{1}{x^2}+\frac{\sin ^3 x+\cos ^3 x}{\sin ^2 x \cos ^2 x}\right) d x=\)TS EAMCET 2025 Medium
More PYQs from TS EAMCET
- If \(A+B+C=\frac{\pi}{4}\), then \(4 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}-\cos \frac{\pi}{8}=\)TS EAMCET 2018 Medium
- If \(\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\frac{4 \pi}{3}+\theta\right)\) \(=\alpha \cos 3 \theta\), then \(\alpha\) is equal toTS EAMCET 2016 Hard
- If \(\frac{\pi}{3}, \theta\) are the eccentric angles of the ends of a focal chord of the ellipse \(\frac{x^2}{16}+\frac{y^2}{12}=1\), then \(\tan \theta=\)TS EAMCET 2020 Hard
- If \(a, b\) are real numbers and \(\alpha\) is a real root of \(x^2+12+3 \sin (a+b x)+6 x=0\) then the value of \(\cos (a+b \alpha)\) for the least positive value of \(a+b \alpha\) isTS EAMCET 2025 Hard
- The following statements are given about hydrogen atom. A. The wavelengths of the spectral lines of Lyman series are greater than the wavelength of the second spectral line of Balmer series. B. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.TS EAMCET 2015 Easy
- In which of the following transition metal ion (aquated) is not correctly matched with its colour?TS EAMCET 2025 Easy