AP EAMCET · Maths · Hyperbola
The distance between the tangents of the hyperbola \(2 x^2-3 y^2=6\) which are perpendicular to the line \(x-2 y+5=0\) is
- A \(2 \sqrt{2}\)
- B 4
- C \(\sqrt{2}\)
- D \(3 \sqrt{2}\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Hyperbola: \(\frac{x^2}{3} - \frac{y^2}{2} = 1 \implies a^2=3, b^2=2\) Slope of given line \(x-2y+5=0\) is \(m_1 = \frac{1}{2}\). Slope of tangents \(m = -\frac{1}{m_1} = -2\). Tangent equation: \(y = mx \pm \sqrt{a^2 m^2 - b^2}\) \(y = -2x \pm \sqrt{3(-2)^2 - 2}\)…
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