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Find the equation to the chord of contact of tangents from the point $(5 , 3 )$ to the hyperbola $4x^{2}-6y^{2}=24$

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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 $4xx_1-6yy_1=24$
Step 2:
Here $(x_1,y_1)=(5,3)$
$4\times 5x-6\times 3y=24$
$\Rightarrow 20x-18y=24$
$\Rightarrow 10x-9y=12$
answered Jun 21, 2013 by sreemathi.v

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