The angle between the pair of tangents drawn | vedclass

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Question

(c) The combined equation of the pair of tangents drawn from $(1,2)$ to the ellipse $3{x^2} + 2{y^2} = 5$ is

$(3{x^2} + 2{y^2} - 5)\,(3 + 8 - 5) =

Vedclass · Accepted Answer

${	an ^{ - 1}}(12/\sqrt 5 )$

Vedclass · Answer

(c) The combined equation of the pair of tangents drawn from $(1,2)$ to the ellipse $3{x^2} + 2{y^2} = 5$ is

$(3{x^2} + 2{y^2} - 5)\,(3 + 8 - 5) = {(3x + 4y - 5)^2}$, [using $S'=T^2$]

$ \Rightarrow $ $9\,{x^2} - 24xy - 4{y^2} + ..... = 0$

The angle between the lines given by this equation is

$	an 	heta \, = \,\frac{{2\sqrt {{h^2} - ab} }}{{a + b}}$, where $a = 9,\,h = - 12,\,b = - 4$

$ \Rightarrow $$	an 	heta = 12\sqrt 5 \Rightarrow \,	heta = {	an ^{ - 1}}(12/\sqrt 5 ).$

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

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