TS EAMCET · Maths · Circle
If the line \(a x+b y=1\) is a tangent to the circle \(s_r \equiv x^2+y^2-r^2=0\), then which one of the following is true?
- A \((a, b)\) lies on the circle \(S_1=0\)
- B \((a, b)\) lies inside the circle \(S_{1 / 2}=0\)
- C \((a, b)\) lies outside the circle \(S_2=0\)
- D \((a, b)\) lies on the circle \(S_3=0\)
Answer & Solution
Correct Answer
(A) \((a, b)\) lies on the circle \(S_1=0\)
Step-by-step Solution
Detailed explanation
We have, \(a x+b y=1\) is tangent of circle \(x^2+y^2-r^2=0\) \( \therefore \quad r=\frac{1}{\sqrt{a^2+b^2}} \Rightarrow r^2=\frac{1}{a^2+b^2} \Rightarrow a^2+b^2=\frac{1}{r^2} \) \(r=1,(a, b)\) lie on the circle \(\therefore(a, b)\) lie on the circle when \(S_1=0\)
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