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If the chord of contact of the point $\mathrm{P}(\mathrm{h}, \mathrm{k})$ with respect to the circle $x^2+y^2-4 x-4 y+8=0$ meets the circle in two distinct points and it also makes an angle $45^{\circ}$ with the positive $\mathrm{X}$-axis in the positive direction, then $(\mathrm{h}, \mathrm{k})$ cannot be
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Verified Answer
The correct answer is:
$(1,1)$
Equation chord of contact of the point $(h, k)$ is
$$
\begin{aligned}
& x h+y k-4 \frac{(x+h)}{2}-4 \frac{(y+k)}{2}+8=0 \\
& \Rightarrow(h-2) x+(k-2) y-2 h-2 k+8=0 \\
& \text { Slope }=\tan 45^{\circ}=-\frac{(h-2)}{k-2}=1 \\
& \Rightarrow k-2+h-2=0 \Rightarrow k+h-4=0
...(i)\end{aligned}
$$
Add point are satisfied.
$$
\begin{aligned}
& x h+y k-4 \frac{(x+h)}{2}-4 \frac{(y+k)}{2}+8=0 \\
& \Rightarrow(h-2) x+(k-2) y-2 h-2 k+8=0 \\
& \text { Slope }=\tan 45^{\circ}=-\frac{(h-2)}{k-2}=1 \\
& \Rightarrow k-2+h-2=0 \Rightarrow k+h-4=0
...(i)\end{aligned}
$$
Add point are satisfied.
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