Question

To find the position of the center of circle respect to line $l$and point $l$.

Short answer

This means that the line drawn from $X$ to the center is perpenduclar to $l$ at $X$. .

Step-by-step solution

Step 1. Given information. 

Line $l$; points $X$and $Y$ .

A circle through $Y$and tangent to $l$at $X$ .

Given figure,

 Step 2. Concept   Used.

Observe the figure.

If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the points of tangency.

This means that the line drawn from $X$ to the center is perpendicular to $l$ at $X$.