If tangents are drawn to the ellipse x^2 + 2y | vedclass

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Question

equation of tangent is 

$\frac{x}{a}\cos 	heta  + \frac{y}{b}\sin 	heta  = 1$

$A$ is $\left( {\frac{a}{{\cos 	heta }},0}

Vedclass · Accepted Answer

$\frac{1}{{2{x^2}}} + \frac{1}{{4{y^2}}} = 1$

Vedclass · Answer

equation of tangent is 

$\frac{x}{a}\cos 	heta  + \frac{y}{b}\sin 	heta  = 1$

$A$ is $\left( {\frac{a}{{\cos 	heta }},0} ight)$

$B$ is $\left( {0,\frac{b}{{\sin 	heta }}} ight)$

Let $P\left( {h,k} ight)$ is mid point

$2h = \frac{a}{{\cos 	heta }}$

$2k = \frac{b}{{\sin 	heta }}$

${\cos ^2}	heta  + {\sin ^2}	heta  = 1$

$ \Rightarrow \frac{{{a^2}}}{{4{h^2}}} + \frac{{{b^2}}}{{4{k^2}}} = 1$

$ \Rightarrow \frac{2}{{4{x^2}}} + \frac{1}{{4{y^2}}} = 1$

$ \Rightarrow \frac{1}{{2{x^2}}} + \frac{1}{{4{y^2}}} = 1$

If tangents are drawn to the ellipse $x^2 + 2y^2 = 2$ at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve

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