Question

find the equation of the locus of P ,if the line segment (2,3) and(-1,5) subtends a right angle at P​

Answer 1

Answer:

Step-by-step explanation:

Let coordinates of P be (h,k).

Slope of line joining P and (2,3) = m1​=h−2k−3​

Slope of line joining P and (−1,5) = m2​=h+1k−5​

Now, as a right angle is subtended at P,

m1​=−m2​1​

∴h−2k−3​=−k−5h+1​

∴(k−3)(k−5)+(h+1)(h−2)=0

∴k2−8k+15+h2−h−2=0

∴h2+k2−h−8k+13=0

∴h2−h+0.25+k2−8k+16+13−16.25=0

∴(h−0.5)2+(k−4)2=3.25

Hence, the required locus is (x−0.5)2+(y−4)2=3.25.

Answer 2

Step-by-step explanation:

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