JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The acute angle between the pair of tangents drawn to the ellipse \(2 x^{2}+3 y^{2}=5\) from the point \((1,3)\) is.
- A \(\tan ^{-1}\left(\frac{16}{7 \sqrt{5}}\right)\)
- B \(\tan ^{-1}\left(\frac{24}{7 \sqrt{5}}\right)\)
- C \(\tan ^{-1}\left(\frac{32}{7 \sqrt{5}}\right)\)
- D \(\tan ^{-1}\left(\frac{3+8 \sqrt{5}}{35}\right)\)
Answer & Solution
Correct Answer
(B) \(\tan ^{-1}\left(\frac{24}{7 \sqrt{5}}\right)\)
Step-by-step Solution
Detailed explanation
Equation of tangent to the ellipse \(2 x ^{2}+3 y ^{2}=5\) is \(y = mx \pm \sqrt{\frac{5}{2} m ^{2}+\frac{5}{3}}\) It pass through \((1,3)\) \(3=m \pm \sqrt{\frac{5}{2} m^{2}+\frac{5}{3}}\) \(3\,m^{2}+12\,m-\frac{44}{3}=0\) Let \(\theta\) be the angle between the tangents…
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