JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Two circles each of radius \(5\, units\) touch each other at the point \((1,2)\). If the equation of their common tangent is \(4 \mathrm{x}+3 \mathrm{y}=10\), and \(\mathrm{C}_{1}(\alpha, \beta)\) and \(\mathrm{C}_{2}(\gamma, \delta)\), \(\mathrm{C}_{1} \neq \mathrm{C}_{2}\) are their centres, then \(|(\alpha+\beta)(\gamma+\delta)|\) is equal to .... .
- A \(40\)
- B \(39\)
- C \(10\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(40\)
Step-by-step Solution
Detailed explanation
Slope of line joining centres of circles \(=\frac{4}{3}=\tan \theta\) \(\Rightarrow \cos \theta=\frac{3}{5}, \sin \theta=\frac{4}{5}\) Now using parametric form \(\frac{x-1}{\cos \theta}=\frac{y-2}{\sin \theta}=\pm 5\)…
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