AP EAMCET · Maths · Circle
If the angle between the circles \(x^2+y^2-2 x-4 y+c=0\) and \(x^2+y^2-4 x-2 y+4=0\) is \(60^{\circ}\), then \(c\) is equal to
- A \(\frac{3 \pm \sqrt{5}}{2}\)
- B \(\frac{6 \pm \sqrt{5}}{2}\)
- C \(\frac{9 \pm \sqrt{5}}{2}\)
- D \(\frac{7 \pm \sqrt{5}}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{7 \pm \sqrt{5}}{2}\)
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & \mathrm{C}_1: x^2+y^2-2 x-4 y+c=0 ... (i)\\ & \mathrm{C}_2: x^2+y^2-4 x-2 y+4=0... (ii) \end{aligned}\) So, centre of circle \(\mathrm{C}_1=(1,2), r_1=\sqrt{5-c}\) and centre of circle \(\mathrm{C}_2=(2,1), r_2=1\) Now, angle between the two circles,…
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 \(\int \frac{1}{x\left[(\log x)^2+4 \log x-1\right]} d x=A \log \left[\frac{\log x+B}{\log x+C}\right]+K\) where \(\mathrm{K}\) is the constant of integration, thenAP EAMCET 2023 Hard
- The product of the perpendicular distances from \((1,-1)\) to the pair of lines \(x^2-4 x y+y^2=0\), isAP EAMCET 2018 Easy
- If \(x=3 \cos t\) and \(y=4 \sin t\), then \(\frac{d^2 y}{d x^2}\) at the point \(\left(x_0, y_0\right)=\left(\frac{3}{2} \sqrt{2}, 2 \sqrt{2}\right)\), isAP EAMCET 2018 Medium
- If \(A(4,0)\) and \(B(-4,0)\) are two points, then the locus of a point \(\mathrm{P}\) such that \(\mathrm{PA}-\mathrm{PB}=4\) isAP EAMCET 2023 Easy
- If \(1, z_1, z_2, \ldots, z_{n-1}\) are the \(n\)th roots of unity, \(\left(1-z_1\right)\left(1-z_2\right) \ldots\left(1-z_{n-1}\right)\) is equal toAP EAMCET 2016 Medium
- If \({ }^{10} P_r=604800\) and \({ }^{10} C_r=120\) then \(r=\)AP EAMCET 2022 Easy
More PYQs from AP EAMCET
- When \(4 \mathrm{C}, \mathrm{Q} C\) and \(1 \mathrm{C}\) electrical charges are placed along a straight line of length ' \(l\) ' at 0 , \(\frac{l}{2}\) and \(l\) respectively. The respective values of \(\mathrm{Q}\) so that the net force on \(4 \mathrm{C}\) is zero and
\(1 \mathrm{C}\) is zero separately are (in coulomb)AP EAMCET 2017 Easy - If \(x\) is real, then the minimum value of \(\frac{x^2-x+1}{x^2+x+1}\), isAP EAMCET 2005 Easy
- Digital signalAP EAMCET 2023 Easy
- If \(\int \sqrt[3]{x}\left\{1+\sqrt[3]{x^4}\right\}^{1 / 7} d x=A\left(1+\sqrt[3]{x^4}\right)^B+c\), then value of \(A B\) is equal toAP EAMCET 2021 Medium
- In the common-base configuration, a transistor has current amplification factor 0.95 . If the transistor is used in common-emitter configuration and base current changes by \(2 \mu \mathrm{A}\), then the change in the collector current isAP EAMCET 2018 Medium
- An object is projected such that it has to attain maximum range. Another body is projected to reach maximum height. If both the objects reached the same maximum height, then the ratio initial velocitiesAP EAMCET 2024 Easy