A Seemingly Short and Sweet but Intriguing Christmas Special Circle Problem. (Revised)

Geometry Level 3

Find the equations of the tangents to the circle \({ x }^{ 2 }+{ y }^{ 2 }-2x-6y-10=0\), which is parallel to the line \(y=2x\).


  1. If the equations can be expressed in the form of \(y=2x+a\) and \(y=2x+b\), find the value of \(a+b\).

  2. The Image uploaded is just for display and has no relation to the real question.

  3. I apologize for any inconvenience caused especially for those who created the solutions for removing the earlier similar question as it wasn't properly set. Again, I hope to see great solutions coming up! Merry Christmas.


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