AP EAMCET · Maths · Hyperbola
If a tangent to the hyperbola \(x y=-1\) is also a tangent to the parabola \(y^2=8 x\), then the equation of that tangent is
- A \(3 y+x=2\)
- B \(y=3 x+4\)
- C \(y=x+2\)
- D \(y=2 x+1\)
Answer & Solution
Correct Answer
(C) \(y=x+2\)
Step-by-step Solution
Detailed explanation
Tangent to \(y^2=8x\) is \(y=mx+\frac{2}{m}\). Tangent to \(xy=-1\) is \(y=mx+k'\) where \((k')^2-4m(1)=0 \implies k'=\pm 2\sqrt{m}\). Thus, \(y=mx\pm 2\sqrt{m}\). Equating the constant terms: \(\frac{2}{m} = \pm 2\sqrt{m}\). \(\frac{1}{m} = \pm \sqrt{m}\). Cubing both sides (or…
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