TS EAMCET · Maths · Hyperbola
A rectangular hyperbola passing through \((3,2)\) has its asymptotes parallel to the coordinate axes. If \((1,1)\) is the point of intersection of the two perpendicular tangents of that hyperbola, then its equation is
- A \(x y=x+\frac{1}{y}\)
- B \(x\left(y+1+\frac{1}{x}\right)=1\)
- C \(x(1-y)=y-1\)
- D \(x y=x+y+1\)
Answer & Solution
Correct Answer
(D) \(x y=x+y+1\)
Step-by-step Solution
Detailed explanation
It is given that a rectangular hyperbola whose asymptotes are parallel to coordinate axis and point of intersection of perpendicular tangents (means centre of hyperbola) is \((1,1)\), the equation of hyperbola we can take as \((x-1)(y-1)=k \text {, }\) \(\ldots(\mathrm{i})\)…
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