TS EAMCET · Maths · Hyperbola
The equation of the hyperbola which passes through the point \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) is
- A \(4 x^2+5 x y-6 y^2-11 x+11 y+50=0\)
- B \(4 x^2+5 x y-6 y^2-11 x+11 y-43=0\)
- C \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
- D \(x^2-5 x y-y^2-11 x+11 y-43=0\)
Answer & Solution
Correct Answer
(C) \(4 x^2-5 x y-6 y^2-11 x+11 y+57=0\)
Step-by-step Solution
Detailed explanation
Since, the equation of the hyperbola differs from that of the joint equations of the tangents by a constant, therefore the equation of the hyperbola will be of the form \((4 x+3 y-7)(x-2 y-1)+k=0\) ...(i) \(\therefore\) Since, the hyperbola passes through the point \((2,3)\).…
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