Prove that the line \( y=x+\sqrt{2} a \) touches the circle \( x^{2}+y^{2}=a^{2} \). Also find t...

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Prove that the line \( y=x+\sqrt{2} a \) touches the circle \( x^{2}+y^{2}=a^{2} \). Also find the point of contact.
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