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I don't know how to solve this exercise in Hyperbolic Geometry.

Find the linear equation of hyperbolic line which passes through point $A=(3,4)$ and it is perpendicular to hyperbolic line with linear equation $x^2+y^2=25$ , $ y>0$.

Blue
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Sotiris Z.
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  • To be clear: Is this an exercise in the Upper Half-Plane Model? – Blue Dec 15 '18 at 17:07
  • @Blue yes it is – Sotiris Z. Dec 15 '18 at 17:10
  • @Blue Can you help me? – Sotiris Z. Dec 18 '18 at 20:30
  • Since $A$ is on the given circle, the perpendicular "line" needed is the orthogonal circle through $A$. A neat thing about orthogonal circles: Where they meet, the tangent line to one circle passes through the center of the other. And, here, you know that the center of the target circle is on the $x$-axis. So, figure out where the tangent at $A$ meets the $x$-axis (recall that the tangent at a point is perpendicular to the radius to the point), and you'll have the center of the target circle; the distance from $A$ to that center gives you the radius; from there you can get the equation. – Blue Dec 19 '18 at 02:53

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