Today in our geometry class we were given a class activity. Question: Construct six points that lie on the locus of a point which moves in such a way that it is equidistant from a fixed point and a line at all times. To solve the problem, I identified two points, labelled A and B. I joined them, and through a perpendicular bisector identified a midpoint. On the intersection of the arc above line segment AB, I located a point O, as the centre. With the compass needle on centre O, I constructed a circle. With compass needle on vertex A, constructed a circle. Also on vertex B, constructed a circle. From all the intersections I had, constructed circles. I am NOT sure whether I did a correct construction, will get our books back tomorrow, friends kindly tell me, did I read the question correctly, is there any other method? Thank you for your time friends!!
Constructing points that lie on the locus of a point
- Thread starter Njabs
- Start date
- Joined
- Feb 4, 2004
- Messages
- 16,583
I can't picture this stuff very well, but I'm fairly certain that the blue and bold text above describes a parabola, where the fixed point is the "focus" and the line is the "directrix". So I'm pretty sure that you should have gotten a parabola.
Thanks
Hi staple! Thank you for taking the trouble to help me. the blue text, actually I was trying to use bold (black) to highlight important information it has nothing to do with parabola. I am sorry for any confusion I might have caused. The actual question was simple written in the ordinary black colour. I hope you understand what I mean, once again thank you!
I can't picture this stuff very well, but I'm fairly certain that the blue and bold text above describes a parabola, where the fixed point is the "focus" and the line is the "directrix". So I'm pretty sure that you should have gotten a parabola.
Hi staple! Thank you for taking the trouble to help me. the blue text, actually I was trying to use bold (black) to highlight important information it has nothing to do with parabola. I am sorry for any confusion I might have caused. The actual question was simple written in the ordinary black colour. I hope you understand what I mean, once again thank you!
- Joined
- Feb 4, 2004
- Messages
- 16,583
Okay. If you're not needing to find six points on the parabola (which is the "Question" in what you posted), what are you trying to do? How do the circles and "vertices" relate to the "Question"? Please be complete. Thank you!
Clarification
Once again thank you for taking your time to try to help, stapel. Let me write the question as it was again. Construct six points that lie on the locus of a point which moves in such a way that it is equidistant from a fixed point and a line at all times. Also provide a short description of your construction. The question is about CONSTRUCTION, but not FINDING points. Responding to the question, what I did was to identify two points, A and B, I joined them to give me the line they are talking about, there after to get the fixed point they are talking about I bisected the line segment AB. Above the line segment AB, I used the intersection for my fixed point which I labelled point O as the centre. From this point, O, I constructed a circle which according to my understanding is the locus of point through which I must construct the six points. My problem is that I am not sure whether I did a right thing or understood the question well. I hope this will clarify the confusion I might have caused. Hoping to here from you again friend!
Once again thank you for taking your time to try to help, stapel. Let me write the question as it was again. Construct six points that lie on the locus of a point which moves in such a way that it is equidistant from a fixed point and a line at all times. Also provide a short description of your construction. The question is about CONSTRUCTION, but not FINDING points. Responding to the question, what I did was to identify two points, A and B, I joined them to give me the line they are talking about, there after to get the fixed point they are talking about I bisected the line segment AB. Above the line segment AB, I used the intersection for my fixed point which I labelled point O as the centre. From this point, O, I constructed a circle which according to my understanding is the locus of point through which I must construct the six points. My problem is that I am not sure whether I did a right thing or understood the question well. I hope this will clarify the confusion I might have caused. Hoping to here from you again friend!
Thank you Denis
Thanks my friend, I'll check it!
Hey Jabber, sometimes google can help a lot...
Here's a site that will help on this problem:
http://www.khanacademy.org/partner-...-parabolas-3/v/parabola-focus-and-directrix-1
Scroll down slowly and you'll see lots of goodies
Thanks my friend, I'll check it!