Question

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

Answer 1

Step-by-step explanation:

Let the third vertex be P(x,y)

Let C=(a,0) and B=(−a,0)

Since PCB form a right angled triangle right angled at P, then application of Pythagoras theorem, gives us

(PC)2+(PB)2=(BC)2

[(x−a)2+y2]+[(x+a)2+y2]=4a2

[(x−a)2+(x+a)2)+2y2=4a2

2x2+2y2+2a2=4a2

2x2+2y2=2a2

x2+y2=a2

This represents a circle.