TS EAMCET · Maths · Hyperbola
If the line \(x+y+k=0\) is a normal to the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) then \(k=\)
- A \(\pm \frac{\sqrt{5}}{13}\)
- B \(\pm \frac{13}{\sqrt{5}}\)
- C \(\pm \frac{13}{5}\)
- D \(\pm \frac{5}{13}\)
Answer & Solution
Correct Answer
(B) \(\pm \frac{13}{\sqrt{5}}\)
Step-by-step Solution
Detailed explanation
We know that equation of normal of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is \[ \frac{a^2 x}{x_1}+\frac{b^2 y}{y_1}=a^2-b^2 \] \(\therefore\) Equations of normal to the hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) is…
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