AP EAMCET · Maths · Hyperbola
\(\mathrm{x}+\mathrm{y}+3=0,2 \mathrm{x}-\mathrm{y}+1=0\) are the equations of the asymptotes of a hyperbola. If \((1,-2)\) is a point on this hyperbola, then the equation of its conjugate hyperbola is
- A \(2 x^2+x y-y^2+7 x-2 y-1=0\)
- B \(2 x^2+x y-y^2+7 x-2 y+13=0\)
- C \(2 x^2+x y+y^2-7 x-2 y-1=0\)
- D \(2 x^2+x y+y^2-7 x-2 y+13=0\)
Answer & Solution
Correct Answer
(B) \(2 x^2+x y-y^2+7 x-2 y+13=0\)
Step-by-step Solution
Detailed explanation
Equation of asymptotes: \(L_1 = x+y+3\), \(L_2 = 2x-y+1\) Equation of hyperbola: \(L_1 L_2 = k \Rightarrow (x+y+3)(2x-y+1) = k\) Substitute point \((1,-2)\): \((1-2+3)(2(1)-(-2)+1) = k \Rightarrow (2)(5) = k \Rightarrow k = 10\) Equation of conjugate hyperbola:…
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