What Is the Radius of a Circle Tangent to the X-Axis?

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Homework Help Overview

The problem involves determining the radius of a circle that is tangent to the x-axis, with its center located at the coordinates (–3, 4). The context is within the standard Cartesian coordinate system.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the concept of tangency and its implications for the radius of the circle. There are suggestions to visualize the problem by drawing the circle and considering the relationship between the center and the x-axis. Questions are raised about the definition of radius and its geometric properties in relation to the tangent line.

Discussion Status

The discussion is active, with participants offering insights into the geometric relationships involved. Some guidance has been provided regarding the properties of tangents and radii, but there is no explicit consensus on the solution yet.

Contextual Notes

Participants are exploring the implications of the circle's center and its tangency to the x-axis, with some uncertainty about the definitions and relationships involved. No specific constraints or rules have been mentioned that would limit the discussion.

Loppyfoot
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Here it is:
A circle with center (–3,4) is tangent to the x-axis in the standard (x,y) coordinate plane. What is the radius of this circle?

I have no idea where to start. I know there is some rule about tangency and circles, but I am unsure. Thanks!
 
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If it's tangent to the x-axis, then it touches the x-axis at precisely one point. Try drawing a circle and you should be able to figure out which point it touches the x-axis at
 
You really don't even need to draw a circle; you should be able to intuit the answer. If the mp is (-3,4) and it only touches 1 point on the x-axis, what is the radius. Isnt the (sort of in this case) definition of radius a ray as a line starting from a (mid)point and going infinitiely in one direction, in this case until it touches the axis? Then how far is that?
 
A radius is always perpendicular to a tangent line. Here, the x-axis is a tangent line. Therefore, a radius must be perpendicular to the x-axis. If the center is at (-3, 4), what is the other end of that radius? How long is it?
 

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