AP EAMCET · Maths · Hyperbola
If \(\theta\) is the acute angle between the tangents drawn from the point \((1,1)\) to the hyperbola \(4 x^2-5 y^2-20=0\), then \(\tan \theta=\)
- A \(2 \sqrt{21}\)
- B \(\frac{4}{5}\)
- C \(\frac{\sqrt{7}}{2}\)
- D \(\frac{2}{\sqrt{7}}\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{21}\)
Step-by-step Solution
Detailed explanation
\(\frac{x^2}{5} - \frac{y^2}{4} = 1 \Rightarrow a^2=5, b^2=4\). Point \((x_1, y_1) = (1,1)\). The equation for the slopes of tangents is \(m^2(x_1^2 - a^2) - 2mx_1y_1 + (y_1^2 + b^2) = 0\).…
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