If L_1, L_2 and L_3 are the chords of contact | vedclass

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Question

(A) The equation of the circle is $x^2+y^2=3$. The equation of the chord of contact for a point $(x_1, y_1)$ with respect to the circle $x^2+y^2=r^2$

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concurrent lines

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(A) The equation of the circle is $x^2+y^2=3$. The equation of the chord of contact for a point $(x_1, y_1)$ with respect to the circle $x^2+y^2=r^2$ is given by $xx_1+yy_1=r^2$.For point $(2,0)$,$L_1: 2x+0y=3 \Rightarrow 2x-3=0$.For point $(1,-2)$,$L_2: 1x-2y=3 \Rightarrow x-2y-3=0$.For point $(4,4)$,$L_3: 4x+4y=3 \Rightarrow 4x+4y-3=0$.To check for concurrency,we solve $L_1$ and $L_2$: $x=\frac{3}{2}$,$y=\frac{1}{2}(\frac{3}{2}-3) = -\frac{3}{4}$.Substituting $(\frac{3}{2}, -\frac{3}{4})$ into $L_3$: $4(\frac{3}{2})+4(-\frac{3}{4})-3 = 6-3-3 = 0$.Since the point satisfies $L_3$,the lines are concurrent.

If $L_1, L_2$ and $L_3$ are the chords of contact of the three points $(2,0), (1,-2)$ and $(4,4)$ respectively with respect to the circle $x^2+y^2=3$,then $L_1, L_2$ and $L_3$ are

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