Question

The ends of the hypotenuse of a right angled triangle are (0,6) and (6,0). Find the equation of the locus of its third vertex.

Answer 1

Step-by-step explanation:

Let ABC is a right angled triangle whose hypotenuse is AC and angle B=90°. co ordinate A (6,0) , C (0,6).

Let co ordinate of B (h,k).

Slope of BA (m1)=(0-k)/(6-h)

Slope of BC (m2)=(6-k)/(0-h)

Angle between BA and BC is 90°

m1×m2= -1

(-k)/(6-h)×(6-k)/(-h)= -1

(6k-k^2)/(6h-h^2)=-1

-6h+h^2=6k-k^2

h^2+k^2–6h-6k=0 , Therefore locus of (h,k) is:-

x^2+y^2–6x-6y=0 , answer.