AP EAMCET · Maths · Hyperbola
If the line \(a x+b y+c=0\) is a normal to the curve \(x y=1\), then
- A \(a>0, b>0\)
- B \(a>0, b < 0\)
- C \(a>0, b=0\)
- D \(a < 0, b < 0\)
Answer & Solution
Correct Answer
(B) \(a>0, b < 0\)
Step-by-step Solution
Detailed explanation
Given curve is \(x y=1\) So, \(y=\frac{1}{x}\) ...(i) Differentiating with respect to \(x\), we get, \(x \frac{\mathrm{d} y}{\mathrm{~d} x}+y=0\) \([\because(u v) \prime=u v \prime+u \prime v]\) \(\Rightarrow \quad \frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{y}{x}\) Given line is,…
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