JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If the length of the chord of the circle, \(x^{2}+y^{2}=r^{2}(r>0)\) along the line, \(y-2 x=3\) is \(r\), then \(r^{2}\) is equal to
- A \(\frac{9}{5}\)
- B \(\frac{12}{5}\)
- C \(12\)
- D \(\frac{24}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{12}{5}\)
Step-by-step Solution
Detailed explanation
Let chord \(A B=r\) \(\because \Delta AOM\) is right angled triangle \(\therefore OM =\frac{ r \sqrt{3}}{2}=\) perpendicular distance of line \(AB\) from (0,0) \(\frac{r \sqrt{3}}{2}=\left|\frac{3}{\sqrt{5}}\right|\) \(r^{2}=\frac{12}{5}\)
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