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$The angle between the pair of tangents from the point (1, 2) to the ellipse 3 x^{2} + 2 y^{2} = 5 is$

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a

tan−1⁡125

b

tan−1⁡65

c

tan−1⁡125

d

tan−1⁡(125)

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detailed solution

Correct option is C

The combined equation of the pair of tangents drawn from(1,2) to the ellipse 3x2+2y2=5 is 3x2+2y2−5(3+8−5)=(3x+4y−5)2 Using SS′=T2⇒ 9x2−24xy−4y2+…=0 If angle between these lines is θ , then tan⁡θ=2h2−aba+b , where a=9,h=−12,b=−4⇒ tan⁡θ=125⇒ θ=tan−1⁡125

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