TS EAMCET · Maths · Circle
If the poles of the line \(x-y=0\) with respect to the circles \(x^2+y^2-2 g_i x+c_i^2=0(i=1,2,3)\) are \(\left(\alpha_i, \beta_i\right)\), then \(\sum_{i=1}^3 \frac{\alpha_i+\beta_i}{g_i}=\)
- A 3
- B 6
- C \(\frac{3}{2}\)
- D \(\frac{3}{4}\)
Answer & Solution
Correct Answer
(A) 3
Step-by-step Solution
Detailed explanation
Since equation polar of point \(\left(\alpha_i, \beta_i\right)\) with respect to the circle \(x^2+y^2-2 g_i x+c_i^2=0\) is \(\alpha_i x+\beta_i y-g_i\left(x+\alpha_i\right)+c_i^2=0\) \(\Rightarrow \quad\left(\alpha_i-g_i\right) x+\beta_i y+c_i^2-\alpha_i g_i=0\) Now, on…
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 \(f(x)=\frac{1}{x^2} \int_3^x\left(2 t-3 f^{\prime}(t)\right) d t\), then \(f^{\prime}(3)\) is equal toTS EAMCET 2004 Hard
- If \(\int \frac{(x-1) d x}{(x+1) \sqrt{x^3+x^2+x}}=f(x)+C\), then \(f(1)=\)TS EAMCET 2020 Medium
- The sum of two numbers is 20 . If the product of the square of one number and cube of the other is maximum, then the numbers are :TS EAMCET 2003 Easy
- \(\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\) \[ \left(1+\cos \frac{7 \pi}{8}\right)= \]TS EAMCET 2019 Easy
- If \(A=(1,2), B=(2,1)\) and \(P\) is a variable point satisfying the condition \(|P A-P B|=3\), then the locus of \(P\) isTS EAMCET 2018 Hard
- If \(\mathrm{I}_n=\int \frac{1}{\left(x^2+1\right)^n} d x\), then \(2 n \mathrm{I}_{n+1}-(2 n-1) \mathrm{I}_n=\)TS EAMCET 2025 Medium
More PYQs from TS EAMCET
- For the formation of \(\mathrm{NH}_3(g)\) from its constituent elements, the favourable conditions for its formation areTS EAMCET 2021 Easy
- If \(m_1, m_2, m_3\) and \(m_4\) respectively denote the moduli of the complex numbers \(1+4 i, 3+i, 1-i\) and \(2-3 i\), then the correct one, among the following isTS EAMCET 2008 Hard
- The \(\theta\) is the angle made by the common tangent to the circle \(x^2+y^2=16\) and the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) with positive \(X\)-axis, then \(\cos 2 \theta=\)TS EAMCET 2020 Medium
- When a vibrating tuning fork is placed on a sound box of a sonometer, 8 beats per second are heard when the length of the sonometer wire is kept at \(101 \mathrm{~cm}\) or \(100 \mathrm{~cm}\). Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant)TS EAMCET 2012 Easy
- \(\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=\)TS EAMCET 2023 Easy
- If ( \(h, k\) ) is the internal centre of similitude of the circles \(x^2+y^2+2 x-6 y+1=0\) and \(x^2+y^2-4 x+2 y+4=0\), then \(4 h=\)TS EAMCET 2024 Medium