JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If the circle \(x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in R\) passes through the point \((6,1)\) and its centre lies on the line \(x-2 c y=8\), then the length of intercept made by the circle on \(x\)-axis is.
- A \(\sqrt{11}\)
- B \(4\)
- C \(3\)
- D \(2 \sqrt{23}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{23}\)
Step-by-step Solution
Detailed explanation
Given circle \(x^{2}+y^{2}-2 g x+6 y-19 c=0\) Passes through \((6,1)\) \(12\,g +19 c =43\) Centre \(( g ,-3)\) lies on given line So, \(g +6 c =8\) Solve equation \((1)\) and \((2)\) \(c =1\) and \(g =2\) equation of circle \(x ^{2}+ y ^{2}-4 x +6 y -19=0\) Length of intercept…
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