Question

The ends of the hypotenuse of a right angled traingle are (0,6)and(6,0)find the equation of locus of its third vayrix is

Answer 1

Answer:

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.

plz mark as brainliest