TS EAMCET · Maths · Circle
If the tangents \(x+y+k=0\) and \(x+a y+b=0\) drawn to the circle \(S \equiv x^2+y^2+2 x-2 y+1=0\) are perpendicular to each other and \(k, b\) are both greater than 1 , then \(b-k=\)
- A \(\sqrt{2}\)
- B 0
- C 2
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Slope of \(x+y+k=0\) is \(m_1=-1\) Slope of \(x+a y+b=0\) is \(m_2=-\frac{1}{a}\) \(m_1 m_2=-1 \Rightarrow-1 \times\left(\frac{-1}{a}\right)=-1 \Rightarrow a=-1\) Centre of circle is \((-1,1) \Rightarrow \frac{-1+1+k}{\sqrt{2}}=1 \Rightarrow k=\sqrt{2}\)…
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