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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 |
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Answer» 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. |
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