AP EAMCET · Maths · Circle
If the circles \(x^2+y^2-2 x-2 y-7=0\) and \(x^2+y^2+4 x+2 y+k=0\) cut orthogonally, then the length of their common chord is units
- A 2
- B 5
- C \(\frac{6}{\sqrt{13}}\)
- D \(\frac{12}{\sqrt{13}}\)
Answer & Solution
Correct Answer
(D) \(\frac{12}{\sqrt{13}}\)
Step-by-step Solution
Detailed explanation
Since the given circles \[ x^2+y^2-2 x-2 y-7=0 \text { and } \] \(x^2+y^2+4 x+2 y+k=0\) cut orthogonally, then \[ (-2)(2)+(-2)(1)=k-7 \] \(\Rightarrow \quad-4-2=k-7 \Rightarrow k=1\) So, equation of common chord is \[ 6 x+4 y+8=0 \Rightarrow 3 x+2 y+4=0 \] \(\therefore\) Length…
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 equation of the polar of the point \((\alpha,-1)\) with respect to the circle \(x^2+y^2-4 x-6 y-12=0\) is \(y=\beta\), then \(4(\alpha+\beta)=\)AP EAMCET 2025 Medium
- The mean deviation about the mean for the following data: isAP EAMCET 2022 Easy
- In \(\triangle P Q R, M\) is the mid-point of \(Q R\) and \(C\) is the mid-point of \(P M\). If \(Q C\) when extended meets \(P R\) at \(N\), then \(\frac{|\overrightarrow{Q N}|}{|\overline{C N}|}=\)AP EAMCET 2018 Medium
- If \(A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0\end{array}\right]\), then \(A^{-1}=\)AP EAMCET 2023 Easy
- For the three points \(A(2,0), B(0,2)\) and \(P(1,1)\), suppose \(d\) is the algebraic sum of the distances of \(A\) and \(B\) from a line that passes through \(P\). Then, which of the following is correct?AP EAMCET 2022 Easy
- \(A+B=C \quad \Rightarrow\)
\(\cos ^2 A+\cos ^2 B+\cos ^2 C-2 \cos A \cos B \cos C\) is equal toAP EAMCET 2005 Medium
More PYQs from AP EAMCET
- In Young's double slit experiment, if the distance between the slits is increased to 3 times initial distance, then the ratio of initial and final fringe widths isAP EAMCET 2025 Easy
- The resistance between points A and C in the given network is
AP EAMCET 2024 Easy - Identify the suitable reagent for the reaction given below.
AP EAMCET 2021 Medium - Which air pollutant is responsible for Bhopal gas tragedy?AP EAMCET 2011 Easy
- The yellow colour of chromate ion and orange colour of dichromate ion is due toAP EAMCET 2020 Easy
- If a resistor of resistance \(4 \Omega\), a capacitor of capacitive reactance \(6 \Omega\) and an inductor of inductive reactance \(9 \Omega\) are connected in series with an ac source, then the impedance of the circuit isAP EAMCET 2025 Easy