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

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