AP EAMCET · Maths · Hyperbola
The asymptotes of a hyperbola are parallel to \(2 x+3 y=0\) and \(3 x+2 y=0\). The equation of that hyperbola whose centre is at \((1,2)\) and passing through \((5,3)\) is
- A \((2 x+3 y-8)(3 x+2 y-7)-154=0\)
- B \((2 x-3 y-8)(3 x-2 y-7)-154=0\)
- C \((3 x+2 y-8)(2 x+3 y-7)-154=0\)
- D \((3 x-2 y+8)(2 x+3 y-7)-154=0\)
Answer & Solution
Correct Answer
(A) \((2 x+3 y-8)(3 x+2 y-7)-154=0\)
Step-by-step Solution
Detailed explanation
Asymptotes passing through \((1,2)\) are \(L_1 = 2(x-1)+3(y-2)=0\) and \(L_2 = 3(x-1)+2(y-2)=0\). \(L_1 = 2x+3y-8=0\) \(L_2 = 3x+2y-7=0\) Equation of hyperbola is \(L_1 L_2 = k\). \((2x+3y-8)(3x+2y-7) = k\) Substitute point \((5,3)\): \((2(5)+3(3)-8)(3(5)+2(3)-7) = k\)…
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