If the line 𝒍𝒙+𝒎𝒚=𝟏 is a tangent to the circle 𝒙^𝟐+𝒚^𝟐=𝒂^𝟐, then prove that (𝒍, 𝒎) lies on a circle.

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If the line 𝒍𝒙+𝒎𝒚+𝒏=𝟎 touches the circle 𝒙^𝟐+𝒚^𝟐=𝒂^𝟐, then prove that (𝒍^𝟐+𝒎^𝟐 ) 𝒂^𝟐=𝒏^𝟐. If the line 𝒍𝒙+𝒎𝒚+𝒏=𝟎 touches the circle 𝒙^𝟐+𝒚^𝟐=𝒂^𝟐, then prove that (𝒍^𝟐+𝒎^𝟐 ) 𝒂^𝟐=𝒏^𝟐.
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