AP EAMCET · Maths · Hyperbola
If \(l x+m y=1\) is a normal to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), then \(a^2 m^2-b^2 l^2=\)
- A \(\frac{m^2}{l^2}\left(a^2+b^2\right)^2\)
- B \(\left(l^2+m^2\right)\left(a^2+b^2\right)^2\)
- C \(\frac{l^2}{m^2}\left(a^2+b^2\right)^2\)
- D \(l^2 m^2\left(a^2+b^2\right)^2\)
Answer & Solution
Correct Answer
(D) \(l^2 m^2\left(a^2+b^2\right)^2\)
Step-by-step Solution
Detailed explanation
Given equation of normal, \(l x+m y=1\) \[ y=\frac{-l}{m}+\frac{1}{m} \] Which is of the form \(y=m x+c\) Since, the lines \(y=m x+c\) will be normal to the hyperbola…
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