AP EAMCET · Maths · Hyperbola
If the line \(l x+m y=1\) is a normal to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then \(\frac{a^2}{l^2}-\frac{b^2}{m^2}\) is equal to
- A \(a^2-b^2\)
- B \(a^2+b^2\)
- C \(\left(a^2+b^2\right)^2\)
- D \(\left(a^2-b^2\right)^2\)
Answer & Solution
Correct Answer
(C) \(\left(a^2+b^2\right)^2\)
Step-by-step Solution
Detailed explanation
If \(l x+m y+n=0\) is normal to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) Then \(\frac{a^2}{l^2}-\frac{b^2}{m^2}=\frac{\left(a^2+b^2\right)^2}{n^2}\) Here, \(n=-1\), therefore \(\frac{a^2}{l^2}-\frac{b^2}{m^2}=\left(a^2+b^2\right)^2\).
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