The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

x2 (52)2+y2 (53)2=1Equation of tangent having slope m isy=mx±53m2+53, which passes through (1, 3) and we get m1 + m2 = -4 and m1m2 = 449∴ Acute angle between the tangents is α = tan-1 |m1−m21+m1m2|=tan−1 (2475)

The acute angle between the pair of tangents drawn to the ellipse 2x2 + 3y2 = 5 from the point (1, 3) is

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Maths Class 12th Conic Sections Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

The acute angle between the pair of tangents drawn to the ellipse 2x² + 3y² = 5 from the point (1, 3) is

Option 1 -

$t a n^{- 1} (\frac{16}{7 \sqrt[]{5}})$

Option 2 -

$t a n^{- 1} (\frac{24}{7 \sqrt[]{5}})$

Option 3 -

$t a n^{- 1} (\frac{32}{7 \sqrt[]{5}})$

Option 4 -

$t a n^{- 1} (\frac{3 + 8 \sqrt[]{5}}{35})$

2 Views | Posted 2 months ago

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

$\frac{x^{2}}{{(\sqrt[]{\frac{5}{2}})}^{2}} + \frac{y^{2}}{{(\sqrt[]{\frac{5}{3}})}^{2}} = 1$

Equation of tangent having slope m is

$y = m x \pm \sqrt[]{\frac{5}{3} m^{2} + \frac{5}{3}},$ which passes through (1, 3) and we get m₁ + m₂ = -4 and m₁m₂ = $\frac{44}{9}$

$∴$ Acute angle between the tangents is α = tan^-1 $| \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} | = t a n^{- 1} (\frac{24}{7 \sqrt[]{5}})$

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