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Find the equation to the chord of contact of tangents from the point $(2 , 4 )$ to the ellipse $2x^{2}+5y^{2}=20$

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  • The chord of contact of tangents drawn from the point $(x_1,y_1)$ to the conic $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ is $Axx_1+\large\frac{B}{2}$$(xy_1+yx_1)+Cyy_1+D\large\frac{(x+x_1)}{2}+$$E\large\frac{(y+y_1)}{2}$$+F=0$
Step 1:
The equation is of the form $2xx_1+5yy_1=10$
Step 2:
Here $(x_1,y_1)=(2,4)$
Therefore the equation is $2\times 2x+5\times 4y=20$
$\Rightarrow 4x+20y=20$
$\Rightarrow x+5y=5$
answered Jun 21, 2013 by sreemathi.v

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