Chapter 14.1, Problem 24PSC

To determine

To write an equation for the locus of the points each of which is the vertex of the right angle of a right triangle whose hypotenuse is the segment joining $(-1,0)$ and $(1,0)$

Answer to Problem 24PSC

  $x^2+y^2=1,x\ne \pm 1$

Explanation of Solution

Given:

  $\overline{PT}\perp \overline{PV}$ .

Calculation:

The vertices of the right angles of right triangles whose hypotenuse is the line segment $\overline{BC}$ form a circle whose diameter is $\overline{BC}$ .

  

The circle centered at $(0,0)$ and has a radius of $1$ . The locus of points would not include the points B and C because they can’t be the vertices of right angle when they define the hypotenuse.

, $x^2+y^2=1,x\ne \pm 1$