Tough Locus Problem

  • Thread starter zorro
  • Start date
In summary, to prove that the locus of point P is a hyperbola, we can assume one line to be the y-axis and the other to be y=mx. By finding the length of the perpendicular lines from P to each line, we can set the area of the figure formed equal to a constant. This will result in a relation between the coordinates of P, proving that the locus is a hyperbola.
  • #1
zorro
1,384
0

Homework Statement


From a point P, perpendiculars PM and PN are drawn to two fixed straight lines OM and ON. If the area OMPN, be constant, prove that the locus of P is a hyperbola.


How do we start?
 
Physics news on Phys.org
  • #2
You can, without loss of generality, assume that one line, say OM, is the y-axis, and the other, ON, is given by y= mx for some number m. If P has coordinates [itex](x_0, y_0)[/itex] then the perpendicular to OM is the line [itex]y= y_0[/itex]. The line through P perpendicular to ON is given by [itex]y= -(1/m)(x- x_0)+ y_0[/itex]. You can find its length by finding x such that [itex]y= -(1/m)(x- x_0)+ y_0= mx[/itex], where the two lines cross. Find the area of that figure, as a function of [itex]x_0[/itex] and [itex]y_0[/itex], set it equal to a constant, and see what relation you get between [itex]x_0[/itex] and [itex]y_0[/itex].
 
  • #3
Thanks!
 

1. What is a "Tough Locus Problem"?

A "Tough Locus Problem" is a term used in genetics to describe a situation where a particular gene or trait is difficult to map or locate on a chromosome. This can be due to the gene's location on a complex region of the chromosome or its interaction with other genes.

2. How do scientists approach solving a "Tough Locus Problem"?

Scientists use a variety of techniques such as linkage analysis, genome-wide association studies, and gene mapping to try and identify the location and function of the gene in question. These methods involve analyzing large amounts of data and often require collaboration between researchers.

3. What are some real-world examples of "Tough Locus Problems"?

One example is the search for genetic factors that contribute to complex diseases like diabetes, Alzheimer's, and cancer. These diseases involve multiple genes and environmental factors, making it difficult to pinpoint the exact genetic cause.

4. Why are "Tough Locus Problems" important to solve?

Solving "Tough Locus Problems" can provide valuable insights into the genetic basis of complex traits and diseases. This can lead to the development of more effective treatments and prevention strategies. Additionally, understanding these problems can help scientists better understand the complex mechanisms of genetic inheritance.

5. Is there a standard method for solving "Tough Locus Problems"?

No, there is no one standard method for solving "Tough Locus Problems". Scientists may use a combination of different techniques and approaches to tackle these challenges. It often requires a multidisciplinary approach and the use of advanced technology and computational methods.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
20
Views
2K
Replies
1
Views
278
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
14
Views
2K
Replies
2
Views
306
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
2K
Replies
4
Views
1K
Back
Top