the Find the equation of forms of p of line segment" joining (2, 3) and(-1,5) sutends a right angle at p
Answers
Answered by
1
Answer:
- a line segment formed by joining the points A(2, 3) and B(-1,5) subtends a right angle at P. Therefore the locus of the point P is x² + y² - x - 8y + 13.
Step-by-step explanation:
- hope it helps you!
Answered by
7
Answer:
Let coordinates of P be (h,k).
Slope of line joining P and (2,3) = m
1
=
h−2
k−3
Slope of line joining P and (−1,5) = m
2
=
h+1
k−5
Now, as a right angle is subtended at P,
m
1
=−
m
2
1
∴
h−2
k−3
=−
k−5
h+1
∴(k−3)(k−5)+(h+1)(h−2)=0
∴k
2
−8k+15+h
2
−h−2=0
∴h
2
+k
2
−h−8k+13=0
∴h
2
−h+0.25+k
2
−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.
hope it's helpful for you to learn
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