AP EAMCET · Maths · Circle
The point \((3,-4)\) lies on both the circles \(x^2+y^2-2 x+8 y+13=0 \quad\) and \(x^2+y^2-4 x+6 y+11=0\). Then, the angle between the circles is
- A \(60^{\circ}\)
- B \(\tan ^{-1}\left(\frac{1}{2}\right)\)
- C \(\tan ^{-1}\left(\frac{3}{5}\right)\)
- D \(135^{\circ}\)
Answer & Solution
Correct Answer
(D) \(135^{\circ}\)
Step-by-step Solution
Detailed explanation
Given circles are \(x^2+y^2-2 x+8 y+13=0\) and \(x^2+y^2-4 x+6 y+11=0\). Here, \(C_1=(1,-4), C_2=(2,-3)\), \(\begin{array}{lll} \Rightarrow & & r_1=\sqrt{1+16-13}=2 \\ \text { and } & & r_2=\sqrt{4+9-11}=\sqrt{2} \end{array}\) Now, \(d=C_1 C_2=\sqrt{(2-1)^2+(-3+4)^2}=\sqrt{2}\)…
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 centroid of the triangle formed by the lines and is , then the value of equals_____AP EAMCET 2021 Hard
- The number of different words that can be formed from the letters of the word "INTERMEDIATE" such that two vowels never come together, isAP EAMCET 2020 Easy
- If \(\alpha\) and \(\beta(\alpha>\beta)\) are the multiple roots of the equation \(4 x^4+4 x^3-23 x^2-12 x\) \(+36=0\), then \(2 \alpha-\beta=\)AP EAMCET 2025 Medium
- If the angle between the circles and is thenAP EAMCET 2019 Easy
- The area of the triangle formed by the lines represented by \(3 x+y+15=0\) and \(3 x^2+12 x y-13 y^2=0\) isAP EAMCET 2024 Medium
- The number of solutions of \(\operatorname{Tan}^{-1} 1+\frac{1}{2} \operatorname{Cos}^{-1} x^2-\operatorname{Tan}^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)=0\) isAP EAMCET 2025 Hard
More PYQs from AP EAMCET
- The rank of the following matrix \(A\) is
\[
A=\left[\begin{array}{cccc}
1 & -2 & 3 & -4 \\
2 & 9 & 4 & 5 \\
4 & 5 & 10 & -3 \\
1 & 11 & -1 & 9
\end{array}\right\rfloor
\]AP EAMCET 2018 Medium - If the circle \(x^2+y^2+2 x+3 y+1=0\) cuts another circle \(x^2+y^2+4 x+3 y+2=0\) in \(A\) and \(B\), then the equation of the circle with \(A B\) as a diameter isAP EAMCET 2010 Hard
- The area (in sq. units) of the triangle formed by the lines \(x^2-3 x y+y^2=0\) and \(x+y+1=0\), isAP EAMCET 2014 Medium
- Let \(\triangle\) denote the area of a \(\triangle A B C\). If \(\alpha, \beta, \gamma\) are the lengths of the altitudes of the \(\triangle A B C\), then \(\alpha^{-2}+\beta^{-2}+\gamma^{-2}=\)AP EAMCET 2019 Hard
- A block of mass \(m\) is lying on a rough inclined plane having an inclination \(\alpha=\tan ^{-1}\left(\frac{1}{5}\right)\). The inclined plane is moving horizontally with a constant acceleration of \(a=2 \mathrm{~ms}^{-2}\) as shown in the figure. The minimum value of coefficient of friction, so that the block remains stationary with respect to the inclined plane is (Take, \(g=10 \mathrm{~ms}^{-2}\) )
AP EAMCET 2019 Hard - The variance of the following distribution is
AP EAMCET 2018 Easy