Question

The ends of hypotenuse of a right angle triangle are(a,0),(-a,0) then the locus of third vertex is

Answer 1

Given:

The ends of hypotenuse of a right angle triangle are (a,0) and (-a,0)

To find:

The locus of the third vertex

Calculation:

Let the third vertex of the triangle be B(x,y). The vertices of the hypotenuse are A(a,0) and C(-a,0)

By pythagoras theorem

 (AC)² = (AB)² + (BC)²

 (0-0)²+(-a-a)² = [ (y-0)²+(x-a)² ] +  [ (0-y)²+(-a-x)² ]

 4a² = (x-a)²+y² + (x+a)²+y²

 4a² = [ (x-a)²+(x+a)² ] +y²

 4a² = 2x²+2a²+2y²

 2a² = 2x²+2y²

 a² = x²+y²

Final answer:

The locus of the third vertex is x²+y²=a². This equation represents a circle