TS EAMCET · Maths · Hyperbola
The distance between the tangents drawn to the hyperbola \(3 x^2-y^2=3\), that are parallel to the line \(y=2 x+4\) is
- A \(\frac{4}{\sqrt{5}}\)
- B \(\frac{2}{\sqrt{5}}\)
- C \(\frac{2}{3}\)
- D 1
Answer & Solution
Correct Answer
(B) \(\frac{2}{\sqrt{5}}\)
Step-by-step Solution
Detailed explanation
Given equation of hyperbola \(3 x^2-y^2=3\) \[ \frac{x^2}{1}-\frac{y^2}{3}=1 \] We know that, equation of tangents of slope \(m\) to the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=\mathrm{l}\) is \[ y=m x \pm \sqrt{a^2 m^2-b^2} \] \(\therefore\) Equation of tangents to Eq. (i)…
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