Question

the Find the equation of forms of p of line segment" joining (2, 3) and(-1,5) sutends a right angle at p




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Answer 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!

Answer 2

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