TS EAMCET · Maths · Hyperbola
If \(L_1=0\) and \(L_2=0\) are the asymptotes of the hyperbola \(9 x^2-4 y^2+36 x+8 y-4=0\), then the product of the perpendicular distances from the point \((1,1)\) to the lines, \(L_1=0\) and \(L_2=0\) is
- A \(\frac{32}{13}\)
- B \(\frac{64}{13}\)
- C \(\frac{81}{13}\)
- D \(\frac{162}{13}\)
Answer & Solution
Correct Answer
(C) \(\frac{81}{13}\)
Step-by-step Solution
Detailed explanation
Equation of given hyperbola is \(\begin{aligned} 9 x^2-4 y^2+36 x+8 y-4 & =0 \\ \Rightarrow \quad 9\left(x^2+4 x+4\right)-4\left(y^2-2 y+1\right) & =36\end{aligned}\) \(\Rightarrow \quad 9(x+2)^2-4(y-1)^2=36\) Now, combined equation of the asymptotes of the hyperbola (i) is…
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