Point of contact of conic tangent to a family of lines passing through a point on the axis

Download Geometry Expressions File

Again, we can force the tangency by reflecting one focus in the tangent line and joining the reflection to the other focus, then intersecting the result with the given tangent.

We observe the locus of the tangent point is a circle with the center and radius shown.

Expressions

Name Input
Radius Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Point E Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Locus Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image