AP EAMCET · Maths · Circle
\(C_1\) is the circle with centre at \(O(0,0)\) and radius \(4, C_2\) is a variable circle with centre at \((\alpha, \beta)\) and radius 5 . If the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) has slope \(\frac{3}{4}\) and of maximum length, then one of the possible values of \(\alpha+\beta\) is
- A \(\frac{21}{5}\)
- B \(\frac{3}{5}\)
- C \(\frac{1}{5}\)
- D \(\frac{19}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{5}\)
Step-by-step Solution
Detailed explanation
Equation of circle \(C_1\) be \(x^2+y^2=16\) Equation of circle \(C_2\) be \((x-\alpha)^2+(y-\beta)^2=25\) \(\Rightarrow x^2-2 \alpha x+\alpha^2+y^2-2 \beta y+\beta^2=25\) Equation of common chord is \(C_2-C_1=0\) \(\Rightarrow-2 \alpha x-2 \beta y+\alpha^2+\beta^2=9\) Slope of…
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