AP EAMCET · Maths · Circle
Suppose \(d_1\) and \(d_2\) are respectively the lengths of intercepts of the cirlce \(x^2+y^2=4\) and \(x^2+y^2-10 x-14 y+65=0\) on the line \(2 x-2 y-3=0\). Then, which of the following is true?
- A \(d_1=2 d_2\)
- B \(d_2=2 d_1\)
- C \(d_1=3 d_2\)
- D \(d_1=d_2\)
Answer & Solution
Correct Answer
(D) \(d_1=d_2\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & O A=\frac{|0-0-3|}{\sqrt{2^2+2^2}}=\frac{3}{\sqrt{8}} \\ & A B=\sqrt{2^2-\left(\frac{3}{\sqrt{8}}\right)^2}=\sqrt{4-\frac{9}{8}}=\sqrt{\frac{23}{8}}\end{aligned}\) \(\therefore \quad d_1=2 \sqrt{\frac{23}{8}}\) \(\Rightarrow x^2+y^2-10 x-14 y+65=0\)…
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