JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Consider two circles \(C_1: x^2+y^2=25\) and \(C_2:(x-\) \(\alpha)^2+y^2=16\), where \(\alpha \in(5,9)\). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) be \(\sin ^{-1}\left(\frac{\sqrt{63}}{8}\right)\). If the length of common chord of \(C_1\) and \(C_2\) is \(\beta\), then the value of \((\alpha \beta)^2\) equals
- A \(1550\)
- B \(1560\)
- C \(1575\)
- D \(1570\)
Answer & Solution
Correct Answer
(C) \(1575\)
Step-by-step Solution
Detailed explanation
\(\mathrm{C}_1: \mathrm{x}^2+\mathrm{y}^2=25, \mathrm{C}_2:(\mathrm{x}-\alpha)^2+\mathrm{y}^2=16\) \(5<\alpha<9\). \(\theta=\sin ^{-1}\left(\frac{\sqrt{63}}{8}\right) \) \( \sin \theta=\frac{\sqrt{63}}{8}\) Area of…
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