Let P be any point on the circle x^2+y^2=25. | vedclass

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(C) Let $P(r, s)$ be a point on the circle $x^2+y^2=25$,so $r^2+s^2=25$ $(i)$.The equation of the chord of contact $L$ of point $P$ with respect to th

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$x^2+y^2=400$

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(C) Let $P(r, s)$ be a point on the circle $x^2+y^2=25$,so $r^2+s^2=25$ $(i)$.The equation of the chord of contact $L$ of point $P$ with respect to the circle $x^2+y^2=9$ is given by $xr+ys=9$ $(ii)$.Let $(h, k)$ be the pole of the line $L$ with respect to the circle $x^2+y^2=36$. The equation of the polar of $(h, k)$ with respect to $x^2+y^2=36$ is $xh+yk=36$ $(iii)$.Comparing equations $(ii)$ and $(iii)$,we have $\frac{r}{h} = \frac{s}{k} = \frac{9}{36} = \frac{1}{4}$.Thus,$r = \frac{h}{4}$ and $s = \frac{k}{4}$.Substituting these into equation $(i)$,we get $(\frac{h}{4})^2 + (\frac{k}{4})^2 = 25$.$\frac{h^2+k^2}{16} = 25 \Rightarrow h^2+k^2 = 400$.Therefore,the locus of the pole $(h, k)$ is $x^2+y^2=400$.

Let $P$ be any point on the circle $x^2+y^2=25$. Let $L$ be the chord of contact of $P$ with respect to the circle $x^2+y^2=9$. The locus of the poles of the lines $L$ with respect to the circle $x^2+y^2=36$ is

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